r 


~ti— n.-n    n— n— «v 


REESE  LIBRARY 

<>i-  TIII-: 

UNIVERSITY  OF  CALIFORNIA. 
^(ecevoed 


HARPER'S  SCIENTIFIC  MEMOIRS 

EDITED  BY 

J.  S.  AMES,  PH.D. 

PROFESSOR    OF   PHYSICS    IN    JOHNS   HOPKINS    UNIVERSITY 


I. 

THE   FREE   EXPANSION    OF    GASES 


THE 


FREE  EXPANSION  OF  GASES 


MEMOIRS   BY   GAY-LUSSAC,  JOULE 
AND  JOULE  AND  THOMSON 


TRANSLATED  AND  EDITED 

BY    J.  S.  AMES,  PH.D. 

PROFESSOR    OF    PHYSICS    IN    JOHNS    HOPKINS    UNIVERSITY 


NEW  YORK   AND  LONDON 

HARPER     &    BROTHERS     PUBLISHERS 
1  898 


HARPER'S    SCIENTIFIC   MEMOIRS. 

EDITED    BY 

JOSEPH  S.  AMES,  PH.D., 

PBOFKSSOB   OF   PHYSIOS    IN   JOHNS   HOPKINS  UNIVERSITY. 

THE  FKEE  EXPANSION  OF  GASES.  Memoirs 
by  Gay-Lussac,  Joule,  and  Joule  and  Thomson 
Editor,  JOSEPH  S.  AMKS,  Ph.D.,  Johns  Hopkins 
University. 

FRAUNHOFER'S  PAPERS  ON  PRISMATIC  AND 

DIFFRACTION    SPECTRA.      Editor,   JOSEPH    S. 

AMKS,  Ph.D.,  Johns  Hopkins  University.     (Nearly 

Ready.) 

IN  PREPARATION: 
RONTGEN  RAYS.    Memoirs  by   Routgeu,  Stokes, 

and   J.   J.     Thomson.    Editor,    Prof.    GKOUQE    F. 

BARKER,  University  of  Pennsylvania. 

THE  SECOND  LAW  OF  THERMODYNAMICS. 
Memoirs  by  Carnot,  Clausins,  and  Thomson.  Editor, 
Prof.  W.  F.  MAGIK,  Princeton  University. 

ON  THE  PROPERTIES  OF  IONS.  Memoirs  by 
Kohlransch  and  Hittorf.  Editor,  Dr.  H.  M.  GOOD- 
WIN, Massachusetts  Institute  of  Technology. 

SOLUTIONS.  Memoirs  by  Pfeffer,  Van  t'Hoff,  Raoult. 
Editor,  Dr.  H.  C.  JONES,  Johns  Hopkins  University. 

ON  THE  LAWS  OF  GASES.  Memoirs  by  Boyle, 
Amagat,  Gay-Lussac.  Editor,  Prof.  CARL  BARIIS, 
Brown  University. 

THE  FARADAY  AND  ZEEMAN  EFFECT.  Me- 
moirs by  Faraday,  Kerr,  and  Zeeman.  Editor,  Dr. 
E.  P.  LEWIS,  University  of  California. 

WAVE  THEORY  OF  LIGHT.  Memoirs  by  Young 
and  Fresnel.  Editor,  Prof.  HENRY  CREW,  North- 
western University. 

MEMOIRS  CONCERNING  THE  LAW  OF  GRAV- 
ITATION. Editor,  Prof.  A.  S.  MAOKENZIK,  Bryu 
Mawr  College.  

NEW   YORK   AND    LONDON: 
HARPER  &  BROTHERS,  PUBLISHERS. 


Copyright,  1898,  by  HARPER  &  BROTHERS. 

All  right*  retervtd. 


PKEFACE 


THE  experiments  on  the  changes  of  temperature  which 
gases  experience  when  they  are  allowed  to  expand  under  such 
conditions  as  to  do  no  external  work  are  of  great  importance 
from  two  standpoints  :  1.  Owing  to  the  minuteness  of  the 
change  of  temperature,  it  may  be  assumed  that  the  intrinsic 
energy  of  a  gas  is  almost  entirely  kinetic ;  and  so  conclusions 
may  be  drawn  between  the  mechanical  work  done  in  compress- 
ing a  gas  and  the  rise  of  temperature  produced  ;  2.  Measure- 
ments of  the  minute  changes  lead  to  a  method  of  comparing 
temperatures  as  registered  on  a  gas  -  thermometer  and  those 
which  are  given  on  Thomson's  Absolute  Scale. 

Robert  Mayer  assumed  that  there  was  no  ' ( internal  work  " 
done  in  compressing  a  gas,  and  so  made  a  calculation  for  what 
is  now  called  the  mechanical  equivalent  of  heat.  The  question 
as  to  whether  Mayer  was  acquainted  with  the  experiments  of 
Gay-Lussac  at  the  time  he  made  his  calculation  or  not  has 
long  been  an  open  one  ;  but  it  is  generally  acknowledged  now 
that  he  was  familiar  with  the  results  obtained  by  Gay-Lussac, 
and  so  was  justified  in  his  theoretical  work.  Gay-Lussac  per- 
formed his  experiments  on  the  free  expansion  of  gases  in  the 
year  1807  ;  and  a  translation  of  his  memoir  is  given  in  this 
volume. 

In  1844  Joule  repeated  these  experiments,  being  unacquaint- 
ed with  the  work  of  Gay-Lussac.  His  published  account  of 
his  research  follows.  The  important  bearing  of  Joule's  experi- 
ment upon  the  science  of  Thermodynamics  was  recognized  by 
William  Thomson  (now  Lord  Kelvin)  ;  and  he  began,  in  col- 
laboration with  Joule,  a  more  complete  investigation  of  the 
"  Thermal  Effects  of  Fluids  in  Motion,"  which  lasted  for  many 
years.  The  most  important  of  their  experiments  are  reported 


PREFACE 

in  this  volume.  Thomson  applied  his  dynamical  theory  of 
heat  to  the  results  obtained,  and  thus  secured  comparisons  be- 
tween gas-thermometer  temperatures  and  those  on  an  "abso- 
lute "  scale,  one  of  the  most  important  contributions  of  the 
century  to  physical  science. 


GENERAL  CONTENTS 


PAGE 

Preface v 

First  Attempt  to  Determine  the  Changes  in  Temperature  which  Gases 
Experience  owing  to  Changes  of  Density,  and  Considerations  on1 

their  Capacity  for  Heat.     By  L.  J.  Gay-Lussac 3 

Biographical  Sketch  of  Gay-Lussac 13 

On  the  Changes  of  Temperature  Produced  by  the  Rarefaction  and 

Condensation  of  Air.     By  J.  P.  Joule 17 

Biographical  Sketch  of  Joule 30 

On  the  Thermal  Effects  of  Elastic  Fluids.     By  Professor  William 
Thomson  and  J.  P.  Joule. 
Part  I. 

Abstract 33 

Part  II 35 

Abstract 83 

Part  IV 87 

Abstract 102 

Bibliography 103 

Index.. 105 


FIRST  ATTEMPT  TO  DETERMINE  THE  CHANGES  IN  TEMPERA- 
TURE WHICH  GASES  EXPERIENCE  OWING  TO  CHANGES 
OF  DENSITY,  AND  CONSIDERATIONS  ON  THEIR 
CAPACITY  FOR  HEAT. 

BY 

L.  J.  GAY-LUSSAC,  Meraoires  d'Arcueil,  I.  1807. 

Reprinted  in  Die  Principien  der  Warmelehre. 
E.  MACH.     Leipzig,  1896. 


CONTENTS 

PAGE 

Preliminary  Work 3 

Free  Expansion  of  Atmospheric  Air 4 

Measurement  of  Temperature 6 

Equality  of  Rise  and  Fall  of  Temperature 7 

Law  of  Temperature  Change ';.-.  7 

Efflux  of  Gases 8 

Free  Expansion  of  Hydrogen . .   10 

"           "           "    Carbonic- Acid  Gas 11 

"    Oxygen 11 

Results...                                                                         . ...  12 


FIRST  ATTEMPT  TO  DETERMINE  THE  CHANGES 'IN  TEMPERA- 
TURE WHICH  GASES  EXPERIENCE  OWING  TO  CHANGES  OF 
DENSITY,  AND  CONSIDERATIONS  ON  THEIR  CAPACITY  FOR 
HEAT. 

BY 

GAY-LUSSAC. 

Read  at  the  Institute,  September  15,  1806. 

IN  the  researches  published  by  Mr.  Humboldt  and  myself  on 
eudiometric  methods  and  the  analysis  of  atmospheric  air,  we 
have  noticed  that  the  combustion  produced  by  an  electric  spark 
in  a  mixture  of  oxygen  and  hydrogen  was  not  complete  when 
the  two  gases  were  in  the  ratio  of  10  to  1.  In  this  experiment, 
when  the  excess  of  oxygen  over  and  above  that  necessary  for 
the  saturation  of  the  hydrogen  was  replaced  by  nitrogen,  the 
combustion  stopped  at  almost  exactly  the  same  point  as  before. 
Guided  by  special  considerations,  we  were  led  to  think  that  this 
phenomenon  depended  on  the  fact  that,  since  the  heat  set  free 
in  the  combination  was  absorbed  by  the  parts  of  each  gas  which 
had  not  entered  into  combination,  the  temperature  was  lowered 
below  the  point  necessary  for  combustion,  and,  as  a  consequence, 
combustion  ceased.  Since,  further,  we  saw  that  the  action  of 
nitrogen  in  this  respect  was  almost  identical  with  that  of  oxy- 
gen, we  had  assumed  that  the  reason  why  these  two  gases  stopped 
the  combustion  at  the  same  point  was  because  they  certainly 
had  the  same  capacity  for  heat.  We  were  not  able  to  verify 
our  conjectures  in  the  case  of  other  gases;  but,  as  one  is  natu- 
rally inclined  to  generalize,  we  maintained  the  opinion — I  in 
particular — that  it  was  most  probable  that  all  gases  had  the 
same  capacity  for  heat.  On  my  return  to  Paris,  after  a  journey 
which  I  made  with  Mr.  Humboldt  to  Italy  and  Germany,  I  was 
impatient  to  make  some  more  direct  experiments  in  order  to 
see  to  what  extent  our  first  conjectures  were  well  founded,  be- 
ing convinced  that,  whatever  was  the  result,  I  would  not  have 

0 


MEMOIRS    ON    THE 

worked  in  vain.  I  communicated  my  project  to  Mr.  Berthollet, 
who  encouraged  me  to  execute  it  ;  and  he,  as  well  as  Mr. 
Laplace,  have  taken  the  most  lively  interest  in  it.  If  it  is  nat- 
tering to  me  to  be  able  to  mention  here  the  names  of  these  two 
illustrious  scientists  who  honor  me  with  their  esteem,  it  is  my 
duty  to  state  at  the  same  time  that  I  owe  a  great  deal  to  their 
clear-sighted  advice.  It  was  at  Arcueil,  in  the  laboratory  of 
Mr.  Berthollet,  that  my  experiments  were  made.  They  have 
led  me,  so  far  as  the  capacity  of  gases  is  concerned,  to  results 
quite  unexpected  and  contrary  to  those  which  I  had  suspected, 
and  have  attracted  my  attention  to  several  new  phenomena 
which  appear  to  have  a  most  important  bearing  upon  the  theory 
of  heat. 

Starting  from  the  two  facts — that  all  gases  are  expanded 
equally  by  heat,  and  that  they  occupy  volumes  which  are  in- 
versely proportional  to  the  weights  which  compress  them — I 
thought,  with  Mr.  Dalton,*that  by  putting  them  all  under  the 
same  conditions  and  then  decreasing  by  the  same  amount  the 
pressure  common  to  them  all,  it  would  be  possible  to  see  from 
the  changes  of  temperature  produced  by  the  increase  in  vol- 
ume whether  they  had  or  had  not  the  same  capacities  for  heat, 
It  was  to  this  end  that  I  used  the  following  apparatus  : 

I  took  two  balloon  flasks,  each  having  two  openings  and  each 
of  twelve  litres'  capacity.  Into  one  of  the  openings  of  each 
flask  I  fitted  a  cock,  and  into  the  other  a  very  sensitive  alcohol 
thermometer,  whose  centigrade  degrees  could  easily  be  read  to 
hundredths.  I  at  first  used  an  air  thermometer,  constructed  on 
the  principles  of  Count  Rumford  or  Mr.  Leslie  ;  but  although 
infinitely  more  sensitive  than  the  alcohol  thermometer,  it  was, 
in  several  respects,  inconvenient.  I  can  remedy  these  defects 
now  ;  but  they  made  me  prefer  the  alcohol  thermometer,  be- 
cause it  gave  me  results  which  were  more  comparable  among 
themselves.  In  order  to  avoid  effects  due  to  moisture,  I  in- 
troduced dried  calcium  chloride  into  each  flask.  The  arrange- 
ment of  the  apparatus  for  each  experiment  was  as  follows  : 
Both  flasks  being  exhausted,  and  having  assured  myself  .that 
there  was  no  leakage,  I  filled  one  flask  with  the  gas  upon  which 
I  wished  to  experiment.  About  twelve  hours  later  I  connected 
the  two  flasks  by  a  lead  tube,  and,  opening  the  cocks,  the  gas 

*  Journal  des  Mines,  torn.  13,  p.  257. 
4 


FREE    EXPANSION    OF    GASES 

rushed  into  the  empty  flask  until  equilibrium  of  pressure  was 
established.  During  this  time  the  thermometer  experienced 
changes  which  I  carefully  noted. 

I  began  my  experiments  with  this  apparatus  by  using  at- 
mospheric air  ;  and  I  observed,  with  MM.  Laplace  and  Ber- 
thollet,  that  the  air  on  passing  into  the  empty  flask  from  the 
other  made  the  thermometer  \in  the  former]  rise,  as  several 
physicists  have  previously  noted.  It  was  known  that  when  air 
expands,  owing  to  a  decrease  in  pressure,  it  absorbs  heat;  and, 
vice  versa,  that  on  being  compressed  it  sets  heat  free.  From 
this  fact  several  physicists  had  drawn  the  conclusion  that  the 
capacity  for  heat  of  air  which  is  expanded  is  greater  than  that  of 
compressed  air,  and  that  an  empty  space  should  contain  more 
heat  than  the  same  space  filled  with  air.  Considering  equal 
weights  of  this  fluid  under  different  pressures  and  at  the  same 
temperature,  there  is  no  doubt  but  that  the  more  it  is  expand- 
ed the  more  heat  it  contains,  because  as  it  expands  it  absorbs 
continually.  But  when  we  consider  equal  volumes,  nothing 
justifies  us  in  believing  that  the  same  thing  must  be  true.  If 
in  our  experiment  the  expanded  air  which  remains  in  the  flask 
originally  filled  has  absorbed  heat,  that  which  has  left  the  flask 
has  carried  heat  with  it,  and  it  is  not  proved  that  the  quantity 
of  heat  absorbed  is  greater  than  that  taken  away.  Consequent- 
ly, the  opinion  of  those  who  believe  that  a  vacuum  contains 
more  heat  than  a  space  full  of  air,  an  opinion  which  rests  on 
the  above  considerations  alone,  is  absolutely  unfounded.  We 
cannot  believe,  with  Mr.  Leslie,  that  it  is  the  trace  of  air  left 
in  the  receiver  in  virtue  of  the  imperfect  vacuum  which  gives 
rise  to  all  this  heat,  owing  to  the  great  reduction  of  volume 
which  it  experiences,  as  a  consequence  of  the  air  being  ad- 
mitted. If  this  were  so,  it  would  necessarily  happen  that,  on 
introducing  a  very  small  volume  into  an  absolutely  empty  re- 
ceiver, there  would  be  a  quantity  of  heat  absorbed  nearly  equal 
to  that  set  free  when  the  receiver  is  emptied  of  air  to  this 
same  extent,  and  ^we  let  it  fill  completely.  But,  far  from 
this,  there  is  heat  set  free  in  every  case.  It  may  seem  indiffer- 
ent at  first  sight  whether  it  is  from  a  space  which  is  empty  or 
from  one  filled  with  air  in  a  state  of  great  expansion  that  the 
heat  is  liberated  when  air  enters  into  this  space  ;  but  it  seems 
to  me  that  for  the  theory  of  heat  it  is  of  the  greatest  impor- 
tance to  know  the  source  of  the  heat.  In  my  experiments,  in 

5 


THB 

UNIVERSITY 


MEMOIRS    ON    THE 

spite  of  the  most  perfect  vacuum  which  I  could  produce  in 
my  receiver,  I  have  always  seen  the  thermometer  placed  in  it 
rise  to  a  most  marked  degree  when  air  from  the  other  rushed 
into  it ;  and  I  cannot  avoid  the  conclusion  that  the  heat  does 
not  come  from  the  traces  of  air  which  may  possibly  be  present. 
Being  convinced  of  this  important  fact,  that  the  higher  the 
vacuum  in  a  receiver  so  much  the  greater  is  the  amount  of  heat 
set  free  when  the  exterior  air  enters,  I  sought  to  determine  by 
exact  experiments  what  relation  there  was  between  the  heat 
absorbed  in  one  of  the  receivers  and  that  set  free  in  the  other, 
and  how  these  changes  in  temperature  depended  upon  the  dif- 
ferences in  density  of  the  air.  For  brevity's  sake  I  shall  call 
"No.  1"  the  flask  in  which  is  enclosed  the  gas  which  is  made 
the  subject  of  experiment ;  and  "No.  2,"  that  which  is  empty. 
.It  is  in  the  first  that  cold  is  produced  ;  in  the  second,  heat. 
In  each  experiment  I  have  noted  exactly  the  thermometer  out- 
side and  the  barometer ;  but,  as  one  varied  only  between  19° 
and  21°  C.,  and  the  other  between  Om.755  and  Om.765,  the  cor- 
rections which  should  be  made  to  the  results  are  quite  small, 
and  can  be  neglected.  In  order  to  see  what  connection  there 
was  between  the  densities  of  the  air  and  the  changes  of  tem- 
perature which  are  due  to  differences  of  density,  I  used  in 
succession  air  whose  density  decreased  as  the  numbers  1,  J,  \, 
etc.  In  order  to  do  this,  after  having  made  air  pass  from 
receiver  No.  1  into  the  empty  receiver  No.  2,  I  renewed  the 
vacuum  in  the  latter,  and  waited  until  there  was  complete 
equilibrium  of  temperature  between  them  both.  Since  the 
two  receivers  had  equal  volumes,  the  density  of  the  air  was 
thus  reduced  one-half.  On  opening  the  cocks,  the  air  was  again 
divided  between  the  two  flasks,  and  the  density  was  reduced  to 
one-quarter.  I  could  have  carried  the  reduction  in  a  similar 
manner  to  -J-,  ^,  etc.  ;  but  I  stopped  at  £,  because  below  that 
the  changes  in  temperature,  which  continued  to  diminish, 
could  have  been  observed  accurately  only  with  the  greatest 
difficulty.  The  following  table  contains  the  means  of  the  re- 
sults of  six  experiments  which  I  made  on  atmospheric  air  : 

Density  of  Air  Expressed  Cold  Produced  in  Heat  Produced  in 

by  the  Barometer.  Flask  No.  1.  Flask  No.  2. 

Om.76  0°.61  0°.58 

(K38  0°.34  0°.34 

Om.19  0°.20  0°.20 
6 


FREE    EXPANSION    OF    GASES 

In  this  table  I  give  the  records  of  only  the  means  of  the  re- 
sults, because  the  greatest  variation  above  or  below  this  mean 
have  been  but  0.05,  when  the  density  of  the  air  was  that  ex- 
pressed by  Om.76  ;  and  they  were  much  smaller  when  the  densi- 
ties were  those  expressed  by  Om.38  and  Om.19. 

On  comparing  the  results,  it  is  seen  that  the  heat  absorbed 
by  the  air  of  flask  No.  1  in  the  first  experiment  is  0°.61,  while 
that  liberated  in  receiver  No.  2  is  only  0°.58.  The  difference 
between  these  numbers  is  of  itself  sufficiently  small  to  be  at- 
tributed to  some  circumstance  whose  influence  one  might 
overlook,  or  even  to  errors  of  observation  ;  but,  if  we  consider 
the  results  given  in  the  second  and  third  rows,  we  see  that 
the  temperature  changes  are  exactly  equal  to  each  other.  I 
think,  therefore,  that  I  am  justified  in  concluding  that;  when 
a  given  volume  of  air  is  made  to  pass  from  one  receiver  into 
another  which  is  empty  and  of  the  same  volume,  the  temper- 
ature changes  in  each  receiver  are  the  same. 

The  numbers  0.61,  0.34,  and  0.20,  which  express  these 
changes  of  temperature,  are  not  exactly  in  the  same  ratio  as  the 
densities  of  the  air  ;  they  diminish  according  to  a  law  which  is 
less  rapid.  But  if  we  consider  that  in  each  experiment  the 
time  required  in  order  that  the  entire  effect  should  be  pro- 
duced was  about  two  minutes,  and  that  in  equal  intervals  of 
time  the  coolings  and  heatings  [due  to  external  causes]  increase 
with  the  difference  in  temperature  between  the  media,  we 
understand  why  the  number  0.20  is  more  removed  from  the 
fourth  of  0.61  than  0.34  is  from  the  half.  And  if  we  are  will- 
ing to  admit  this  cause  as  that  which  produces  these  differ- 
ences, we  conclude  that  it  is  probable  that,  when  we  condense 
or  expand  air,  the  changes  in  temperature  which  it  experiences 
are  proportional  to  the  differences  of  density. 

If,  then,  the  number  0.20  has  been  less  affected  by  the 
sources  of  error  than  the  others,  it  must  be  more  exact  than 
they  ;  and,  consequently,  in  accordance  with  the  ratio  just 
established,  the  number  0.61,  which  expresses  the  change  in 
temperature  of  air  when  its  density  is  Om.76,  is  too  small — it 
should  be  at  least  0.80. 

Nevertheless,  this  last  number  does  not  yet  express  exactly 
all  the  heat  which  has  been  absorbed  or  set  free.  To  gain 
an  idea  of  this  quantity,  it  would  be  necessary  to  take  into  ac- 
count the  masses  of  the  receivers  and  the  thermometer,  which 

7 


MEMOIRS    ON    THE 

are  considerable  in  comparison  with  the  mass  of  the  air.  An 
air  thermometer  placed  in  the  same  conditions  as  the  alcohol 
one  indicated  5°.0  instead  of  0°.G1,  as  given  by  the  latter. 

As  I  must  return  later  to  this  subject,  after  performing  ex- 
periments which  will  be  specially  directed  to  this  end,  I  shall 
say  no  more  about  the  matter  now.  I  shall  note  merely  that 
the  heat  liberated  or  absorbed  is  very  large  compared  with  the 
mass  of  the  air. 

In  order  to  avoid  the  effects  of  moisture,  I  was  obliged  to 
use  two  receivers,  in  one  of  which  was  placed  calcium  chloride. 
But  when  I  made  the  exterior  air  enter  directly  into  the  empty 
receiver,  the  thermometric  effects  were  nearly  doubled — a  fact 
in  accord  with  the  law  which  we  have  just  established. 

This  law,  that  the  thermometric  effects  follow  the  same 
ratio  as  the  densities  of  the  air,  leads  us  to  conclude  that  on 
suddenly  diminishing  or  increasing  a  perfectly  empty  space  no 
change  of  temperature  would  be  produced.  I  have  diminished 
the  vacuum  space  of  a  large  barometer  in  which  I  placed  one  of 
the  bulbs  of  a  sensitive  air  thermometer,  and  neither  by  inclin- 
ing the  barometer  nor  by  then  raising  it  erect  did  I  perceive, 
a  change  of  temperature. 

After  these  experiments  it  was  extremely  interesting  to  know 
what  would  happen  with  hydrogen,  whose  specific  gravity  is  so 
different  from  that  of  atmospheric  air.  I  filled  receiver  No.  1 
with  this  gas,  and,  after  leaving  it  twelve  hours  in  contact  with 
calcium  chloride,  during  which  time  I  took  care  to  allow  from 
time  to  time  gas  to  enter,  so  as  to  fill  the  space  left  by  the 
moisture  as  it  was  absorbed,  I  opened  the  communication  with 
the  empty  receiver  No.  2.  The  flow  of  the  hydrogen  was  in- 
stantaneous compared  with  that  of  air,  and  the  changes  of  tem- 
perature were  much  greater.  The  opening  of  communication 
between  the  two  receivers  had  remained  the  same  for  the  two 
gases  ;  and  considering  the  great  difference  between  their  spe- 
cific gravities,  it  was  not  difficult  to  recognize  in  this  the  true 
cause  of  the  inequality  of  the  times  of  escape.  When,  in  fact, 
two  fluids  compressed  to  the  same  extent  escape  by  two  small 
openings  of  the  same  size,  their  velocities  vary  inversely  as  the 
square  root  of  their  densities.  If,  then,  it  is  desired  in  our 
experiments  to  make  the  times  of  escape  the  same,  the  openings 
must  be  made  inversely  proportional  to  the  square  roots  of  the 
densities. 

8 


FREE    EXPANSION    OF    GASES 

Making  use  of  these  principles,  Mr.  Leslie  has  devised  a 
most  elegant  method  for  measuring  the  specific  gravities  of 
elastic  fluids.  Let  us  imagine  a  bag  full  of  gas,  and  commu- 
nicating by  means  of  a  cock  which  has  a  small  opening  with  a 
bell- jar  full  of  water  and  inverted  over  a  large  bath  of  the  same 
liquid.  When  the  cock  is  opened  the  gas  passes  out  of  the 
bag  into  the  receiver,  because  there  is  no  longer  equilibrium 
of  pressure,  and  a  certain  time  is  required  for  it  to  depress  the 
water  and  make  it  come  down  to  a  definite  point.  On  noting 
the  time  required  by  each  gas  to  make  the  water  reach  the  same 
mark,  the  specific  gravities  will  vary  directly  as  the  squares  of 
these  times.* 

In  order  to  compare  the  effects  of  different  gases  with  refer- 
ence to  the  changes  in  temperature  which  they  can  produce  in 
changing  volume,  it  was  necessary  to  make  the  conditions  the 
same  for  them  all,  and,  consequently,  to  modify  my  apparatus. 
First  of  all,  it  was  necessary  to  have  a  means  of  measuring  the 
time  of  escape  for  a  given  opening,  and  then  to  have  a  means 
of  varying  the  openings  in  order  to  make  the  time  of  escape 
constant. 

To  satisfy  the  first  requirement  I  placed  a  small  disk  of 
paper,  2  cm.  in  diameter,  under  the  opening  of  the  cock  of  the 
empty  flask.  This  disk  is  supported  by  a  ring  of  iron  wire, 
carrying  a  small  prolongation  to  serve  as  a  lever  and  to  bear  a 
counterpoise.  Two  silk  threads  serve  as  the  axis  of  the  lever, 
and  tend  by  a  slight  torsion,  which  can  be  given  them,  to  bring 
the  disk  back  into  a  horizontal  position,  in  which  a  stop  pre- 
vents it  from  going  farther  in  that  direction.  When  a  gas 
enters  the  flask  it  strikes  the  disk,  makes  it  take  a  vertical  posi- 
tion, in  which  there  is  a  second  stop  preventing  further  motion, 
and  the  time  taken  for  the  escape  of  the  gas  is  measured  by 
that  taken  by  the  disk  to  return  to  its  horizontal  position. 

In  order  to  vary  the  size  of  the  opening  at  will  I  had  Mr. 
Fortin  construct  for  me  a  small  piece  of  apparatus,  which  I  shall 
briefly  describe.  It  is  a  metallic  disk  in  which  there  is  an  open- 
ing bounded  by  two  concentric  circles  and  by  two  radii,  making 
an  angle  slightly  less  than  180°.  A  second  disk,  which  is  semi- 
circular, turns  with  friction  over  the  first,  and  in  various  posi- 

*  An  Experimental  Inquiry  into  the  Nature  and  Propagation  of  Heat.  By 
J.  Leslie,  p.  534. 

9 


MEMOIRS    ON    THE 

tions  cuts  off  more  or  less  of  the  opening.  By  means  of  this 
arrangement  and  of  divisions  engraved  on  the  edge  of  each 
disk,  it  is  easy  to  make  the  opening  vary  at  will,  and  by  a 
quantity  which  is  perfectly  definite. 

As  in  my  experiments  on  atmospheric  air  I  had  not  noted  the 
time,  I  began  them  again  with  this  object  in  view  ;  and  I  found 
that  the  time  of  escape  was  always  eleven  seconds.  This  time 
did  not  vary  with  the  density  of  the  air  ;  and  although  this  is 
the  way  it  should  be,  it  is  none  the  less  interesting  to  see  the 
theory  so  well  confirmed  by  experiment. 

For  hydrogen,  I  then  diminished  tfye  opening  until  the  time 
of  escape  was  the  same  as  that  for  atmospheric  air.  In  spite  of 
this  equality  of  circumstances  the  changes  in  temperature  were 
most  different,  as  can  be  seen  from  the  means  of  the  results  of 
four  experiments : 

Density  of  Hydrogen  Cold  Produced  in  Heat  Produced  in 

Expressed  by  Barometer.  Flask  No.  1.  Flask  No.  2. 

Om.76  0°.92  0°.77 

Om.38  0°.54  0°.54 

The  cold  produced  in  the  flask  in  which  the  hydrogen  was, 
instead  of  being  0°.61  as  for  atmospheric  air,  was  0°.92  ;  and  the 
heat,  instead  of  being  0°.58,  was  found  to  be  0°.77.  The  differ- 
ence between  0°.92  and  0°.77  is  much  greater  than  that  between 
0°.61  and  0°.58  ;  but  as  it  is  not  probable  that  the  changes  in 
temperature  for  hydrogen  follow  a  different  law  from  those  for 
air,  I  am  inclined  to  believe  that  the  difference  between  0°.77 
and  0°.92  is  due  solely  to  some  condition  of  the  experiment.  We 
will  see,  in  fact,  that  when  the  temperatures  differ  less  in  either 
direction  from  that  of  the  surrounding  medium,  there  is  a  bet- 
ter agreement. 

The  density  of  hydrogen  being  reduced  one-half  in  the  two 
flasks,  I  exhausted  No.  2,  and  after  the  re-establishment  of 
uniform  temperature  I  opened  communication  with  No.  1.  I 
speak  here  of  but  one  experiment :  but  it  is,  in  fact,  the  mean  of 
the  results  of  four  experiments  which  I  consider.  The  heat 
absorbed  was  0°.54,  and  that  liberated  was  also  0°.54.  This 
number  is  greater  than  one-half  of  0°.92,  the  figure  obtained  in 
the  first  experiment,  and  the  difference  is  greater  than  that 
presented  by  the  two  corresponding  numbers  0°.34  and  0°.61, 
of  the  experiments  on  atmospheric  air,  a  fact  which  seems  to  me 
to  confirm  the  idea  that  when  the  changes  in  temperature  are 

10 


FREE    EXPANSION    OF    GASES 

very  great,  the  errors  are  also  the  greatest.  It  seems  to  me, 
then,  that  when  hydrogen  changes  its  volume,  owing  to  an  in- 
crease or  decrease  of  the  weight  which  compresses  it,  the  result- 
ing changes  in  temperature  obey  the  same  law  as  do  those 
experienced  by  air,  but  that  the  former  are  much  greater. 

I  call  to  mind  here  that  Mr.  Leslie,  whose  work  on  heat  con- 
tains some  most  beautiful  experiments  and  many  new  ideas, 
was  led  into  error  in  some  way  when  he  saw  that  hydrogen  ad- 
mitted into  a  receiver  exhausted  of  air  to  nearly  one-tenth  pro- 
duced the  same  effect  as  did  air  itself  if  admitted  in  its  place. 
We  have  just  seen  that  the  changes  of  temperature  which  these 
two  elastic  fluids  produce  are  most  different,  and  that,  conse- 
quently, the  conclusion  which  he  has  drawn,  that  they  contain 
in  equal  volumes  the  same  quantity  of  heat,  falls  of  itself.* 

Having  determined,  as  well  as  I  could,  the  temperature 
changes  which  accompany  those  of  density  in  hydrogen,  I  be- 
gan the  investigation  of  carbonic  acid. 

Having  ascertained  by  preliminary  trials  the  size  of  opening 
which  gave  a  time  of  escape  of  eleven  seconds,  as  in  the  case  of 
hydrogen  and  air,  I  performed  the  experiments  in  the  same 
way  as  for  the  other  gases,  and  formed  in  the  same  manner  the 
following  table,  which  includes  the  means  of  the  results  of  five 
experiments.  It  should  be  noticed  that  when  carbonic  acid 
rushed  into  the  empty  flask,  it  produced  a  loud,  hissing  sound. 
This  is  in  general  greater  for  gases  of  greater  specific  gravity. 

Density  of  Carbonic  Acid  Cold  Produced  in  Heat  Produced  in 
Gas  Expressed  by                            Flask  No.  1.  Flask  No.  2. 

the  Barometer. 

Om.76  0°.56  0°.50 

Om.38  0°.30  0°.31 

The  changes  in  temperature,  either  positive  or  negative,  are 
nearly  equal,  as  we  see,  and  follow  the  law  of  densities  ;  but 
they  are  smaller  than  those  for  air,  and,  therefore,  all  the  more 
so,  smaller  than  those  for  hydrogen. 

Likewise,  oxygen  has  given,  in  a  single  experiment,  it  is  true, 
but  in  one  made  with  great  care,  the  following  results  : 

Density  of  Oxygen  Ex-  Cold  Produced  in  Heat  Produced  in 

pressed  by  the  ,  Flask  No.  1.  Flask  No.  2. 

Barometer. 

Om.76  0°.58  0°56 

Om.38  0°.31  0°.32 

*  An  Experimental  Inquiry,  etc.,  p.  533. 
11 


MEMOIRS    ON    THE 

Up  to  the  present  time  I  have  been  unable  to  extend  my  in- 
vestigations further.  If  we  compare,  however,  the  results  which 
we  have  obtained,  we  will  be  in  a  condition  to  deduce  some  new 
conclusions  as  a  result  of  those  already  announced. 

We  see  that,  all  circumstances  being  the  same,  the  tempera- 
ture changes  produced  by  changes  in  volume  are  greater,  the 
smaller  the  specific  gravity  of  the  gas.  These  changes  are  less 
for  carbonic  acid  than  for  oxygen,  less  for  oxygen  than  for  at- 
mospheric air,  and  much  less  for  this  last  than  for  hydrogen, 
which  is  the  lightest  of  all.  Moreover,  if  we  note  that  all  gases 
are  expanded  to  the  same  extent  by  heat,  and  that  in  our  experi- 
ments, on  occupying  larger  volumes  (but  the  same  for  all), 
they  absorbed  quantities  of  heat  which  were  inversely  propor- 
tional to  their  specific  gravities,  we,  draw  the  important  con- 
clusion that  the  capacities  for  heat  of  gases,  for  equal  volumes, 
increase  as  their  specific  gravities  decrease. 

My  experiments  have  not  yet  given  me  the  exact  law  of  this 
connection.  I  think,  however,  that  it  may  be  determined ;  and 
I  hope  to  make  it  the  subject  of  a  special  investigation. 

Of  all  known  gases,  hydrogen  ought  then  to  have  the  great- 
est capacity  for  heat,  if  I  am  not  deceived  by  the  results  of  my 
experiments.  Since,  further,  oxygen  and  nitrogen  differ  only 
slightly  in  specific  gravity,  it  would  follow  that  they  would 
have  nearly  the  same  capacity  for  heat.  This  is  the  reason 
why,  in  the  memoir  already  quoted,  on  the  analysis  of  air,  we 
had  found  that  these  two  gases  stop  the  combustion  of  hydro- 
gen at  nearly  the  same  point.  This  is  also  the  reason  why,  as 
I  have  found  recently,  hydrogen  stops  it  sooner  than  oxygen 
or  nitrogen.  It  would  be  interesting  to  know  exactly  the  in- 
fluence of  each  gas  in  stopping  the  combustion  of  hydrogen ; 
and  I  am  hoping  to  make  some  new  researches  on  this  sub- 
ject. 

On  collecting  the  various  results  which  I  have  stated  in  this 
memoir,  I  think  I  can  present  as  very  probable  the  following 
consequences,  which  naturally  spring  from  them  : 

1st.  When  a  gas  is  made  to  occupy  an  empty  space,  the  heat 
set  free  is  not  due  to  the  traces  of  air  which  can  be  supposed  to 
have  been  present. 

2d.  If  we  join  two  equal  spaces,  one  empty,  the  other  full  of 
a  gas,  the  thermometric  changes  which  take  place  in  each  are 
the  same. 

12 


FREE    EXPANSION    OF    GASES 

3d.  For  the  same  gas,  these  temperature-changes  are  propor- 
tional to  the  changes  in  density  which  are  experienced. 

4th.  These  temperature  -  changes  are  not  the  same  for  all 
gases.  They  are  greater  the  smaller  the  specific  gravities. 

5th.  The  capacities  of  the  same  gas  for  heat  diminish  with 
the  density,  the  volume  being  the  same. 

6th.  The  capacities  of  gases  for  heat,  for  equal  volumes, 
are  greater  the  smaller  the  specific  gravities. 

I  think  I  may  repeat  that  I  present  these  conclusions  only 
with  great  reserve,  knowing,  myself,  how  I  need  to  vary  my 
experiments,  and  how  easy  it  is  to  go  astray  in  the  interpreta- 
tion of  results ;  but  although  the  new  researches  to  which 
they  lead  me  are  immense,  I  will  not  allow  myself  to  be  stopped 
owing  to  their  difficulty. 

BIOGRAPHICAL  SKETCH. 

Louis  Joseph  Gay-Lussac  was  born  in  St.  Leonard,  Limousin, 
December  6,  1778,  and  died  in  Paris,  May  9,  1850.  He  was 
educated  at  the  iScole  Polytechnique  and  the  ficole  des  Ponts- 
et-Chaussees  ;  and  became  Professor  of  Chemistry  at  the  ficole 
Polytechnique,  and  Professor  of  Physics  in  the  Sorbonne. 

His  most  important  scientific  researches  were  the  following  : 

1.  The  discovery  of  simple  volume  relations  in  the  formation 
of  chemical  compounds. 

2.  The  laws  of  expansion  of  gases  with  change  of  tempera- 
ture. 

3.  The  discovery  of  boron  and  cyanogen,  and  his  famous  in- 
vestigation of  iodine. 

4.  The  invention  of  the   siphon  -  barometer,  and  numerous 
meteorological  investigations. 


ON  THE  CHANGES  OF  TEMPERATURE  PRODUCED  BY  THE  RARE- 
FACTION AND  CONDENSATION  OF  AIR. 

BY  JAMES  PRESCOTT  JOULE, 
Phil.  Mag.,  Series  3,  XXVI.,  p.  369,  1845  ;  Scientific  Papers,  Vol.  I.,  p.  172. 


CONTENTS 

PAGE 

Previous  Work 17 

Apparatus  and  Method 18 

Compression  of  Gas.     Eise  of  Temperature 20 

Mechanical  Equivalent  of  Heat 23 

Expansion  of  Gas.     Equality  of  Rise  and  Fall  of  Tem- 
perature   26 

Expansion  against  Atmospheric  Pressure 27 

Mechanical  Equivalent  of  Heat 28 

Conclusions 29 


ON   THE   CHANGES   OF    TEMPERATURE    PRODUCED    BY   THE 
KAREFACTION  AND  CONDENSATION  OF  AIR. 

BY  J.  P.  JOULE,  ESQ.* 

IN  a  paper  f  which  was  read  before  the  Chemical  Section  of 
the  British  Association  at  Cork,  I  applied  Dr.  Faraday's  fine 
discovery  of  magneto-electricity  in  order  to  establish  definite 
relations  between  heat  and  the  ordinary  forms  of  mechanical 
power.  In  that  paper  it  was  demonstrated  experimentally  that 
the  mechanical  power  exerted  in  turning  a  magneto-electrical 
machine  is  converted  into  the  heat  evolved  by  the  passage  of 
the  currents  of  induction  through  its  coils ;  and,  on  the  other 
hand,  that  the  motive  power  of  the  electro-magnetic  engine  is 
obtained  at  the  expense  of  the  heat  due  to  the  chemical  re- 
actions of  the  battery  by  which  it  is  worked.  I  hope,  at  a 
future  period,  to  be  able  to  communicate  some  new  and  very 
delicate  experiments,  in  order  to  ascertain  the  mechanical 
equivalent  of  heat  with  the  accuracy  which  its  importance  to 
physical  science  demands.  My  present  object  is  to  relate  an 
investigation  in  which  I  believe  I  have  succeeded  in  successful- 
ly applying  the  principles  before  maintained  to  the  changes  of 
temperature  arising  from  the  alteration  of  the  density  of  gas- 
eous bodies — an  inquiry  of  great  interest  in  a  practical  as  well 
as  theoretical  point  of  view,  owing  to  its  bearing  upon  the  the- 
ory of  the  steam-engine. 

Dr.  Cullen  and  Dr.  Darwin  appear  to  have  been  the  first  who 
observed  that  the  temperature  of  air  is  decreased  by  rarefac- 
tion and  increased  by  condensation.  Other  philosophers  have 
subsequently  directed  their  attention  to  the  subject.  Dalton 


*  The  experiments  were  made  at  Oak  Field,  Whalley  Range,  near  Man- 
chester. 

f  Phil  Mag.,  Series  3,  Vol.  XXIII.,  pp.  263,  347,  435.     [1843.] 
B  17 


MEMOIRS    ON    THE 

was,  however,  the  first  who  succeeded  in  measuring  the  change 
of  temperature  with  some  degree  of  accuracy.  By  the  employ- 
ment of  an  exceedingly  ingenious  contrivance,  that  illustrious 
philosopher  ascertained  that  about  50°  of  heat  are  evolved  when 
air  is  compressed  to  one-half  of  its  original  bulk,  and  that,  on 
the  other  hand,  50°  are  absorbed  by  a  corresponding  rarefac- 
tion.* 

There  is  every  reason  for  believing  that  Dalton's  results  are 
very  near  the  truth,  especially  as  they  have  been  exactly  con- 
firmed by  the  experiments  of  Dr.  Ure  with  the  thermometer  of 
Breguet.  But  our  knowledge  of  the  specific  heat  of  elastic 
fluids  is  of  such  an  uncertain  character  that  we  should  not  be 
justified  in  attempting  to  deduce  from  them  the  absolute  quan- 
tity of  heat  evolved  or  absorbed.  I  have  succeeded  in  remov- 
ing this  difficulty  by  immersing  my  condensing -pump  and 
receiver  into  a  large  quantity  of  water,  so  as  to  transfer  the 
calorific  effect  to  a  body  which  is  universally  received  as  the 
standard  of  capacity. 

My  apparatus  will  be  understood  on  inspecting  Fig.  1.  C 
represents  the  condensing  -  pump,  consisting  of  a  cylinder  of 
gun-metal  and  of  a  piston  fitted  with  a  plug  of  oiled  leather, 
which  works  easily,  yet  tightly,  through  a  stroke  of  8  inches. 
The  cylinder  is  10J  inches  long,  If  inches  in  interior  diameter, 
and  £  of  an  incji  in  thickness  of  metal.  The  pipe  A,  for  the 
admission  of  air,  is  fitted  to  the  lower  part  of  the  cylinder  ;  at 
the  bottom  of  this  pipe  there  is  a  conical  valve,  constructed  of 
horn,  opening  downward.  A  copper  receiver,  R,  which  is  12 
inches  long,  \\  inches  in  exterior  diameter,  J  of  an  inch  thick, 
and  has  a  capacity  of  136J  cubic  inches,  may  be  screwed  upon 
the  pump  at  pleasure.  This  receiver  is  furnished  with  a  conical 
valve  of  horn  opening  downward,  and  at  the  bottom  with  a 
piece  of  brass,  B,  along  the  centre  of  which  there  is  a  bore  of 
\  of  an  inch  diameter.  There  is  a  stopcock  at  S  which  I  shall 
describe  more  particularly  in  the  sequel. 

Anticipating  that  the  changes  of  temperature  of  the  large 
quantity  of  water  which  was  necessary,  in  order  to  surround  the 
receiver  and  pump,  would  be  very  minute,  I  was  at  great  pains 
in  providing  a  thermometer  of  extreme  sensibility  and  very 

*  Memoirs  of  the  Literary  and  Philosophical  Society  of  Manchester,  Vol. 
V.,  Part  2,  pp.  251-525. 

13 


FREE    EXPANSION    OF    GASES 

great  accuracy.  A  glass  tube  of  narrow  bore  having  been 
selected,  a  column  of  mercury,  1  inch  long,  was  introduced, 
and  gradually  advanced  in  such  a  manner  that  the  end  of  the 


FIG.  1.     Scale, 


column  in  one  position  coincided  with  the  beginning  of  the 
column  in  the  next.  In  each  position  the  length  of  the  column 
was  ascertained  to  the  -^^  part  of  an  inch,  by  means  of  an 
instrument  invented  for  the  purpose  by  Mr.  Dancer.*  After- 
wards the  tube  was  covered  with  a  film  of  beeswax,  and  each  of 
the  previously  measured  spaces  was  divided  into  twenty  equal 
parts  by  means  of  a  steel  point  carried  by  the  dividing  instru- 
ment ;  it  was  then  etched  by  exposure  to  the  vapor  of  fluoric 

*  Of  the  firm  of  Abraham  &  Dancer,  Cross  Street,  Manchester.  I  have 
great  pleasure  in  acknowledging  here  the  skill  displayed  by  this  gentleman 
in  the  construction  of  the  different  parts  of  my  apparatus.  To  it  I  must,  in 
a  great  measure,  attribute  whatever  success  has  attended  the  experiments 
detailed  in  this  paper. 

19 


MEMOIRS    ON    THE 

acid.  The  scale  thus  formed  was  entirely  arbitrary  ;  and  as  it 
only  extended  between  30°  and  90°,  it  was  necessary  to  compare 
the  thermometer  with  another,  constructed  in  the  same  manner, 
but  furnished  with  a  scale  including  the  boiling  as  well  as  the 
freezing  point.  When  this  was  done  it  was  found  that  ten 
divisions  of  the  sensible  thermometer  (occupying  about  £  an 
inch)  were  nearly  equal  to  the  degree  of  Fahrenheit  ;  there- 
fore, since  by  practice  I  can  easily  estimate  with  the  naked  eye 
3*0  of  each  of  these  divisions,  I  could  with  this  instrument  de- 
termine temperatures  to  the  -g-J-^  part  of  a  degree.  The  scale 
being  arbitrary,  the  indications  of  the  thermometer  had  to  be 
reduced  in  every  instance,  a  circumstance  which  accounts  for 
my  having  given  the  temperatures  in  the  tables  to  three  places 
of  decimals. 

It  was  important  to  employ,  for  the  purpose  of  containing 
the  water,  a  vessel  as  impermeable  to  heat  as  possible.  With 
this  view,  two  jars  of  tinned  iron — one  of  them  every  way  an 
inch  smaller  than  the  other — having  been  provided,  the  smaller 
jar  was  placed  within  the  larger  one,  and  the  interstice  between 
the  two  was  closed  hermetically.  By  this  means  a  stratum  of 
air  of  very  nearly  the  same  temperature  as  the  water  was  kept 
in  contact  with  the  sides  and  bottom  of  the  inner  jar.  The 
jars  used  in  the  other  experiments  which  I  shall  bring  forward 
were  constructed  in  a  similar  manner.  Among  other  precau- 
tions to  insure  accuracy,  proper  screens  were  placed  between 
the  vessels  of  water  and  the  experimenter. 

My  first  experiments  were  conducted  in  the  following  man- 
ner :  The  pump  and  copper  receiver  were  immersed  in  45  Ib. 
3  oz.  of  water,  into  which  the  very  sensible  thermometer  above 
described  was  then  placed,  while  two  other  thermometers  were 
employed  in  order  to  ascertain  the  temperature  of  the  room 
and  that  of  the  water  contained  by  the  vessel  W.  Having 
stirred  the  water  thoroughly,  its  temperature  was  carefully 
read  off.  The  pump  was  then  worked  at  a  moderate  degree  of 
speed  until  about  22  atmospheres  of  air,  dried  by  being  passed 
through  the  vessel  G,  full  of  small  pieces  of  chloride  of  calcium, 
were  compressed  into  the  copper  receiver.  After  this  opera- 
tion (which  occupied  from  fifteen  to  twenty  minutes)  the  water 
was  stirred  for  five  minutes  so  as  to  diffuse  the  heat  equally 
.through  every  part,  and  then  its  temperature  was  again  read  off. 

The  increase  of  temperature  thus  observed  was  owing  partly 

20 


FREE    EXPANSION    OF    GA 


to  the  condensation  of  the  air,  and  partly  also  to  the  friction  of 
the  pump  and  the  motion  of  the  water  during  the  process  of 
stirring.  To  estimate  the  value  of  the  latter  sources  of  heat, 
the  air-pipe  A  was  closed,  and  the  pump  was  worked  at  the  same 
velocity  and  for  the  same  time  as  before,  and  the  water  was  after- 
wards stirred  precisely  as  in  the  first  instance.  The  consequent 
increase  of  temperature  indicated  heat  due  to  friction,  etc. 

The  jar  was  now  removed,  and  the  receiver,  having  been  im- 
mersed into  a  pneumatic  trough,  the  quantity  of  air  which  had 
been  compressed  into  it  was  measured  in  the  usual  manner  and 
then  corrected  for  the  force  of  vapor,  etc.  The  result  added  to 
136.5  cubic  inches,  the  quantity  contained  by  the  receiver  at 
first,  gave  the  whole  quantity  of  compressed  air. 

The  result  given  in  Table  I.  is  the  difference  between  the 
effects  of  condensation  and  friction  alone,  corrected  for  the 
slight  superiority  of  the  cooling  influence  of  the  atmosphere  in 
the  experiments  on  friction.  We  must  now,  however,  proceed 
to  apply  a  further  correction  on  account  of  the  circumstance 
that  the  friction  of  the  piston  was  considerably  greater  during 
the  condensing  experiments  than  during  the  experiments  to 
ascertain  the  effect  of  friction.  In  the  latter  case  the  piston 
worked  with  a  vacuum  beneath  it,  while  in  the  former  the 
leather  was  pressed  to  the  sides  of  the  pump  by  a  force  of  con- 
densed air  averaging  32  Ib.  per  square  inch.  I  endeavored  to 

TABLE   I. 


»>S 

It 

in 

<D*S 

•5-j 

fl 

• 

Temperatu 

re  of  Water 

1 

•= 

Source  of  Heat 

in 

z£ 

Baromet 
Pressu 

11 

i< 

H3 

H05 

II 

2 

in 

a 

Before  Ex- 
periment 

After  Ex- 
periment 

Heat  0 

Condensation,  etc.. 
Friction,  etc  
Condensation,  etc.  . 
Friction,  etc  
Condensation,  etc.. 
Friction  etc  

300 
300 
300 
300 
300 
300 

30.06 
30.07 
30.24 

3047 
2924 

2870 

0 

56.2 
54.8 
53.7 

0 

57.5 
57.5 
53.5 
54.5 
52.5 
52.6 

0 

2.224— 
1.685— 
0.817+ 
0.358+ 
0.380+ 
0.760+ 

54.930 
55.652 
53.970 
54.675 
52.562 
53.  197 

55.622 
55.979 
54.664 
55.042 
53.197 
53.524 

0.692 
0.327 
0.694 
0.367 
0.635 
0.327 

Condensation,  etc.. 
Friction,  etc  
Condensation,  etc.. 
Friction,  etc  

300 
300 
300 
300 

30.07 
30.34 

2939 
2924 

58.8 
55.7 

57.5 
57.75 
53.5 
53.75 

1.794— 
1.536— 

2.184+ 
2.316+ 

55.359 
56.053 
55.409 
55.962 

5li.  053 
56.375 
55.959 
56.170 

0.694 
0.322 
0.550 
0.20S 

Condensation,  etc.  . 
Friction,  etc  

300 
300 

30.  •» 

3033 

58.1 

(50.0 
60.4 

0.174+ 
0.196+ 

59.876 
60.478 

60.472 
60.713 

0.596 
0.235 

Condensation,  mean 
Friction,  etc.  ,  mean. 

300 
300 

30.20 

2956 

56.2 

0.078— 
0.068+ 

0.643 
0.297 

Corrected  Result.  .  . 

30.20 

1 

2956 

0.344 

21 


MEMOIRS    ON    THE 


estimate  the  difference  between  the  friction  in  the  two  cases 
by  removing  the  valve  of  the  receiver  and  working  the  pump 
with  about  32  Ib.  per  square  inch  pressure  below  it.  These 
experiments,  alternated  with  others  in  which  a  vacuum  was 
beneath  the  piston,  showed  that  the  heat  given  out  in  the  two 
cases  was,  as  nearly  as  possible,  in  the  ratio  of  six  to  five. 
When  the  correction  indicated  in  this  manner  has  been  applied 
to  0°.297  (see  Table)  and  the  result  subtracted  from  0°.643,  we 
obtain  0°.2S5  as  the  effect  of  compressing  2956  cubic  inches  of 
dry  air  at  a  pressure  of  30.2  inches  of  mercury  into  the  space  of 
136.5  cubic  inches. 

This  heat  was  distributed  through  45  Ib.  3  oz.  of  water,  20-^ 
Ib.  of  brass  and  copper,  and  6  Ib.  of  tinned  iron.  It  was  there- 
fore equivalent  to  13°.  628  per  Ib.  avoirdupois  of  water. 

The  force  necessary  to  affect  the  above  condensation  may  be 
easily  deduced  from  the  law  of  Boyle  and  Mariotte,  which  has 
been  proved  by  the  French  academicians  to  hold  good  as  far  as 
the  twenty-fifth  atmosphere  of  pressure.  Let  Fig.  2  represent 


FIG.  2. 


P 


168.5  Ib. 


(M 


3648.7  Ib. 

,a  cylinder  closed  at  one  end,  the  length  of  which  is  21.654  feet, 
and  the  sectional  area  11.376  square  inches.  Then  one  foot  of 
it  will  have  exactly  the  same  capacity  as  the  copper  receiver 
used  in  the  experiments,  and  its  whole  capacity  will  be  2956 
cubic  inches.  It  is  evident,  therefore*  that  the  force  used  in 

22 


FREE    EXPANSION    OF    GASES 


pumping  (considered  to  be  without  friction)  was  exactly  equal 
to  that  which  would  push  the  piston  p  to  the  distance  of  a  foot 
from  the  bottom  of  the  cylinder.  Excluding  exterior  atmos- 
pheric pressure,  the  force  upon  the  piston,  when  at  the  top  of 
the  cylinder,  will  be  168.5  lb.,  the  weight  of  a  column  of  mer- 
cury 30.2  inches  long  and  of  11.376  square  inches' section  ;  and 
at  a  foot  from  the  bottom  it  will  be  21.654  times  as  much,  or 
3648.7  lb.  The  hyperbolic  area,  abed,  will  therefore  rep- 
resent the  force  employed  in  the  condensation,  including  the 
assistance  of  the  atmospheric  pressure.  Applying  the  formula 
for  hyperbolic  spaces,  we  have 

5=3648.7  x 2.302585  x log  21.654=11220.2. 

The  force  expended  in  condensation  was  therefore  equivalent 
to  that  which  can  raise  11220.2  lb.  to  the  perpendicular  height 
of  one  foot. 

Comparing  this  with  the  quantity  of  heat  evolved,  we  have 
|^| -ff|  =-8~f£  So  that  a  mechanical  force  capable  of  raising 
823  lb.  to  the  height  of  one  foot  must  be  applied  in  the  con- 
densation of  air  in  order  to  increase  the  '  temperature  of  a 
pound  of  water  by  one  degree  of  Fahrenheit's  scale. 

The  following  table  contains  the  results  of  experiments  similar 
to  the  last,  except  in  the  extent  to  which  the  compression  of 
air  was  carried. 

TABLE  II. 


Source  of  Heat 

Number  of 
Strokes  of 
Pump 

Barometrical 
Pressure 

QuantltyofAir 
Compressed  hi 
Cubic  Inches 

Temp,  of  the 
Air  Admitted 

Mean  Temp, 
of  the  Room 

5 

Temperature  of  Water 

Hcut  Gained 

Before  Ex- 
periment 

After  Ex- 
periment 

Condensation,  etc.. 

120 
120 
120 
120 
120 
120 
120 
120 
120 
120 

120 
120 

30.40 
30.50 
30.50 
30.57 
29.94 

1410 
1467 
1440 
1442 
1405 

0 

54.0 
56.6 
62.6 
59.0 
55.2 

o 
54.2 
54.6 
56.5 
56.7 
63.6 
64.0 
58.4 
58.5 
57.0 
57.2 

0.010+ 
0.224— 
0.308+ 
0.281+ 
1.763— 
1.960— 
0.400+ 
0.477+ 
1.566— 
1.573— 

54.099 
54.332 
56693 
56.926 
61.703 
61.976 
58.680 
58.921 
55.310 
55.563 

54.322 
54.421 
56.923 
57.036 
61.971 
62  105 
58.921 
59.033 
55.558 
55.692 

O 
0.  223 
0.089 
0.230 
0.110 
0.268 
0.129 
0.241 
0.112 
0.248 
0.129 

Condensation,  etc. 
Friction,  etc  
Condensation,  etc. 
Friction,  etc  
Condensation,  etc. 
Friction,  etc  
Condensation,  etc. 
Friction,  etc  

Condensation,  mean 
Friction,  etc.,  mean 

30.38 

1433 

57.5 

0.522— 
0.600— 

0.242 
0.114 

Corrected  Result... 

30.38 

1433 

0.128 

23 


MEMOIRS    ON    THE 

After  applying  the  proper  correction  for  the  increase  of  fric- 
tion during  condensation,  and  reducing  the  result,  as  before, 
to  the  capacity  of  a  pound  of  water,  I  find  5°. 26  to  be  the  mean 
quantity  of  heat  evolved  by  compression  of  air  in  the  above 
series  of  experiments. 

The  mechanical  force  expended  in  the  condensation  is  repre- 
sented in  this  instance  by 

5  =  1779.3  x  2.302585  x  log  10.498=4183.46. 

Hence  the  equivalent  of  a  degree  of  heat  per  pound  of  water, 
as  determined  by  the  above  series,  is  795  Ib.  raised  to  the 
height  of  one  foot. 

The  mechanical  equivalents  of  heat  derived  from  the  fore- 
going experiments  were  so  near  838*  Ib.,  the  result  of  mag- 
netical  experiments  in  which  "latent  heat"  could  not  be  sus- 
pected to  interfere  in  any  way,  as  to  convince  me  that  the  heat 
evolved  was  simply  the  manifestation  in  another  form  of  the 
mechanical  power  expended  in  the  act  of  condensation.  I  was 
still  further  confirmed  in  this  view  of  the  subject  by  the  follow- 
ing experiments. 

I  provided  another  copper  receiver  (E,  Fig.  3)  which  had  a 

FIG.  3. 


capacity  of  134  cubic  inches.  Like  the  former  receiver,  to 
which  it  could  be  connected  by  a  coupling  nut,  it  had  a  piece 
D  attached,  in  the  centre  of  which  there  was  a  bore  -J-  of  an 
inch  diameter,  which  could  be  closed  perfectly  by  means  of 
a  proper  stopcock. 


*Phil.  Mag.,  Series  3,  Vol.  XXIII.,  p.  441. 
24 


FREE    EXPANSION    OF    GASES 


I  must  here  be  permitted  to  make  a  short  digression,  in  order 
to  explain  the  construction  of  the  stopcocks,  as  it  may  save 
those  who  shall  in  future  attempt  similar  experiments  the  use- 
less trouble  of  trying  to  make  the  ordinary  stopcock  perfectly 
air-tight  under  pressures.  The  one  I  have  used  is  the  inven- 
tion of  Mr.  Ash,  of  this  town,  a  gentleman  well  known  for  his 
great  mechanical  genius  ;  and  he  has  in  the  most  obliging  man- 
ner allowed  me  to  give  a  full  description  of  it.  Fig.  4  is  a  full- 


FIG.  4. 


sized  sectional  view  of  the  stopcock,  a  is  a  brass  screw,  by 
means  of  which  a  thick  collar  of  leather,  I,  is  very  tightly  com- 
pressed. The  centre  of  a  is  perforated  with  a  female  screw,  in 
which  a  steel  screw,  S,  works,  the  threads  of  which  press  so 
tightly  against  the  leather  collar  as  effectually  to  prevent  any 
escape  of  air  in  that  direction.  The  end  of  the  steel  screw  is 
smooth  and  conical,  and  the  conical  hole  h  is  plugged  with  tin. 
When  the  stopcock  is  shut,  the  smooth  end  of  the  steel  screw 
presses  against  the  soft  metal,  so  as  to  prevent  the  escape  of 
the  least  particle  of  air ;  but  when  opened,  as  represented  in 
the  figure,  it  leaves  a  passage  for  the  air  around  the  conical 
point.  I  have  tested  this  stopcock  in  the  most  severe  manner, 
and  have  found  it  to  answer  perfectly. 

Having  filled  the  receiver  R  (Fig.  3)  with  about  22  atmos- 

25 


MEMOIRS    ON    THE 


j)heres  of  dry  air,  and  having  exhausted  the  receiver  E  by 
means  of  an  air-pump,  I  screwed  them  together,  and  then  put 
them  into  a  tin  can  containing  16J  Ib.  of  water.  The  water 
was  first  thoroughly  stirred,  and  its  temperature  taken  by  the 
same  delicate  thermometer  which  was  made  use  of  in  the  for- 
mer experiments.  The  stopcocks  were  then  opened  by  means 
of  a  proper  key,  and  the  air  allowed  to  pass  from  the  full  into 
the  empty  receiver  until  equilibrium  was  established  between 
the  two.  Lastly,  the  water  was  again  stirred  and  its  tempera- 
ture carefully  noted.  The  following  table  contains  the  results 
of  a  series  of  experiments  conducted  in  this  way,  alternated 
with  others  to  eliminate  the  effects  of  stirring,  evaporation,  etc.  : 

TABLE  III. 


1, 

.£  c  c 

gj 
B<~ 

I 

Temperatur 

e  of  Water 

Nature  of  Experiment 

|pH 

Jill 

*  • 

|H 

1 

5 

Before 
Experiment 

After 
Experiment 

of  Heat 

Expansion  
Alternation  

30.20 

2910 

o 
57.4 
57  0 

0 

0.118+ 
0  906 

57.520 
56  085 

O 

57.517 
56  103 

o 
0.003    loss 
0  018  ga  11 

Expansion  
Alternation  

30.44 

2920 

57.0 
62  0 

0.885— 
0  783 

56.  103 
61  217 

56.128 
61  217 

0.025      ' 

o 

Expansion  
Alternation  

30.44 

2910 

62.1 
58  5 

0.873— 
0  233+ 

61.222 
58  732 

61.232 
58  735 

0.010 
0  003 

30  44 

2915 

58  6 

0  132+ 

58  732 

58  732 

Q 

Alternation  

61  3 

0  787 

60  508 

60  518 

0  010 

30  46 

3200 

61  3 

0  780 

60  518 

60  523 

0  005 

Alternation  .... 

58  0 

0  186+ 

58  184 

58  187 

0  003 

30  50 

2880 

58  3 

0  110  - 

58  190 

KO  ion 

Mean    of   ExperM 
mentsof  Expau-  > 
sion  ) 

30.41 

2956 

0.400— 

0.0062  gain 

Mean  of  Alternations 

0.411— 

0.0068  gain 

Corrected  Result... 

30.41 

2956 

0 

The  difference  between  the  means  of  the  expansions  and  al- 
ternations being  exactly  such  as  was  found  to  be  due  to  the  in- 
creased effect  of  the  temperature  of  the  room  in  the  latter  case, 
we  arrive  at  the  conclusion  that  no  change  of  temperature  oc- 
curs when  air  is  allowed  to  expand  in  such  a  manner  as  not  to 
develop  mechanical  power. 

In  order  to  analyze  the  above  experiments,  I  inverted  the  re- 
ceivers, as  shown  in  Fig.  5,  and  immersed  them,  as  well  as  the 
connecting  piece,  into  separate  cans  of  water.  One  of  the  re- 
ceivers had  2828  cubic  inches  of  dry  air  condensed  into  it, 

26 


FREE    EXPANSION    OF    GASES 


while  the  other  was  vacuous.     After  equilibrium  was  restored 
by  opening  the  cocks,  I  found  that  2°. 36  of  cold  per  Ib.  of 


FIG.  5. 


water  had  been  produced  in  the  receiver  from  which  the  air 
had  expanded,  while  2°. 38  of  heat  had  been  produced  in  the 
other  receiver,  and  0°.31  of  heat  also  in  the  can  in  which  the 
connecting  piece  was  immersed,  the  sum  of  the  whole  amount- 
ing nearly  to  zero.  The  slight  redundance  of  heat  was  owing 
to  the  loss  of  cold  during  the  passage  of  the  air  from  the 
charged  receiver  to  the  stopcocks,  through  a  part  of  the  pipe 
which  could  not  be  immersed  in  water. 

A  series  of  experiments  was  now  made  in  the  following  man- 
ner :  The  receiver  was  filled  with  dry,  compressed  air,  and  a 
coiled  leaden  pipe,  £  of  an  inch  in  internal  diameter  and  12 
yards  long,  was  screwed  tightly  upon  the  nozzle,  as  represented 
in  Fig.  6.  The  whole  was  then  immersed  into  an  oval  can, 
which  was  constructed  as  before  described,  and  was  also  cov- 
ered at  top  as  perfectly  as  possible.  Having  ascertained  the 

FIG.  6. 


MEMOIRS    ON    THE 


temperature  of  the  water  by  means  of  the  sensible  thermome- 
ter before  used,  the  stopcock  was  opened  and  the  air  made  to 
pass  from  the  receiver  through  a  pneumatic  trough  into  a  jar, 
by  which  it  was  carefully  measured.  After  the  air  in  the  re- 
ceiver had  been  reduced  to  the  atmospheric  pressure,  the  water 
was  again  well  stirred,  and  its  temperature  noted.  An  alter- 
nation was  made  after  each  of  these  experiments,  in  order  to 
eliminate  the  effects  of  stirring,  etc. 

TABLE  IV. 


"8  a, 

"*! 

.!: 

< 

y 

Temperatu 

e  of  Water 

Nature  of 

i! 

U 

y 

1=3 

Experiment 

li 

>.  £ 

•s  £• 

*H  15 

HM 

£ 

I 

Gain  or  Loss 
of  Heat 

1* 

si 

^j 

§3j 

Q 

Before 

After 

« 

so 
<y 

1 
9 

Jtt 

Experiment 

Experiment 

0 

0 

0 

O 

0 

Expansion.  . 

30.04 

2862 

2726 

55.7 

0.405+ 

56.207 

56.004 

0.203  loss 

Alternation  . 

55.4 

0.5794- 

56.004 

55.954 

0.050  loss 

Expansion.  . 

30.10 

2807 

2670 

54.0 

0.022+ 

54.714 

54.530 

0.184  loss 

Alternation. 

54.25 

0.27(i+ 

54.536 

54.516 

0.020   loss 

Expansion.  . 

30.10 

2723 

2587 

53.6 

0.760+ 

54.460 

54.259 

0.201   loss 

Alternation. 

53.4 

0.839+ 

54.259 

54.219 

0.040   loss 

Expansion.. 

30.10 

2807 

2670 

49.05 

0.307+ 

49.456 

49.258 

0.198  loss 

Alternation  . 

49.1 

0.158+ 

49.258 

49.258 

0 

Expansion.  . 

30.23 

3039 

2903 

50.6 

0.508+ 

50.176 

50.008 

0.168   loss    i 

Alternation  . 

51.1 

1.063— 

50.017 

50.057 

0  040  gain 

Expansion. 

30.20 

2919 

2782 

49.0 

0.355— 

48.728 

48.563 

0.165  loss 

Alternation.   . 

48.85 

0.277— 

49.573 

48.573 

0 

MeanofExpe  1 

riments   of  > 

30.13 

2859 

2723 

0.105+ 

0.1865  loss 

Expansion  .  ) 

Mean    of  Al-  ) 
teruations  .  ) 

0.085+ 

0.01  17  loss 

Corrected  Re-) 
suit  / 

30.13 

2859 

2723 

0.1738  loss 

The  cold  produced  was  diffused  through  21.17  Ib.  of  water, 
14  Ib.  of  copper,  8  Ib.  of  lead,  and  7  Ib.  of  tinned  iron. 
Hence  we  find  that  a  quantity  of  cold  was  produced  in  the  ex- 
periments sufficient  to  cause  the  temperature  of  a  pound  of 
water  to  decrease  by  4°. 085.  At  the  same  time  a  mechanical 
force  was  developed  which  could  raise  a  column  of  the  atmos- 
phere of  an  inch  square  at  the  base  to  the  altitude  of  2723 
inches  ;  or,  in  other  words,  could  raise  3352  Ib.  to  the  height 
of  one  foot.  For  each  degree  of  heat  lost  there  was  therefore 
generated  a  force  sufficient  to  raise  820  Ib.  to  the  height  of  one 
foot. 

In  the  two  following  series  the  experiments  were  varied  by 

28 


FREE    EXPANSION    OF   GASES 

compressing  and  measuring  out  different  volumes  of  air. 
[Omitted.] 

These  results  are  inexplicable  if  heat  be  a  substance.  If  that 
were  the  case,  the  same  quantity  of  heat  would  have  been  ab- 
sorbed by  the  rarefaction  which  took  place  in  the  experiments  of 
Table  IV.  as  was  evolved  by  the  corresponding  condensation  in 
the  experiments  of  Table  I. ;  also  a  certain  quantity  of  cold 
would  have  been  produced  in  the  experiments  given  in  Table 
III.  The  results  are,  however,  such  as  might  have  been  de- 
duced a  priori  from  any  theory  in  which  heat  is  regarded  as  a 
state  of  motion  among  the  constituent  particles  of  bodies.  It 
is  easy  to  understand  how  the  mechanical  force  expended  in 
the  condensation  of  air  may  be  communicated  to  these  particles 
so  as  to  increase  the  rapidity  of  their  motion,  and  thus  may 
produce  the  phenomenon  of  increase  of  temperature.  In  the 
experiments  of  Table  III.  no  cold  was  produced,  because  the 
momentum  of  these  particles  was  not  permanently  converted 
into  mechanical  power,  but  had  the  motion  of  the  air  from  one 
vessel  to  the  other  been  opposed  in  such  a  manner  as  to  develop 
power  at  the  outside  of  the  jar,  which  might  have  been  accom- 
plished by  means  of  a  cylinder  and  piston,  then  loss  of  heat 
would  have  occurred,  just  as  in  Tables  IV.,  V.,  and  VI.,  where 
the  force  was  applied  in  lifting  the  atmosphere  of  the  earth. 

It  is  quite  evident  that  the  reason  why  the  cold  in  the  exper- 
iments of  Table  IV.  was  so  much  inferior  in  quantity  to  the 
heat  evolved  in  those  of  Table  I.  is  that  all  the  force  of  the 
air  over  and  above  that  employed  in  lifting  the  atmosphere 
was  applied  in  overcoming  the  resistance  of  the  stopcock,  and 
was  there  converted  back  again  into  its  equivalent  of  heat. 

The  discovery  of  Dulong*  that  equal  volumes  of  all  elastic 
fluids,  taken  at  the  same  temperature  and  under  the  same  tem- 
perature, when  suddenly  compressed  or  dilated  to  the  same 
fraction  of  their  volume,  disengage  or  absorb  the  same  absolute 
quantity  of  heat  accords  perfectly  with  these  principles. 

The  mechanical  equivalents  of  heat  determined  by  the  vari- 
ous series  of  experiments  given  in  this  paper  are  823,  795,  820, 
814,  and  760.  The  mean  of  the  last  three,  which  I  take  as  least 
liable  to  error,  is  798  lb.,  a  result  so  near  838  lb.,  the  equiva- 
lent which  I  deduced  from  my  magnetical  experiments,  as  to 

*  Annales  de  Chimie,  Vol.  XLL,  p.  156. 
29 


FREE    EXPANSION    OF    GASES 

confirm  in  a  remarkable  manner  the  above  explanation  of  the 
phenomena  described  in  this  paper,  and  to  afford  a  new,  and, 
to  my  mind,  powerful  argument  in  favor  of  the  dynamical  the- 
ory of  heat  which  originated  with  Bacon,  Newton,  and  Boyle, 
and  has  been  at  a  later  period  so  well  supported  by  the  experi- 
ments of  Rumford,  Davy,  and  Forbes.  [ Tivo  pages  omitted.] 

OAK  FIELD,  NEAR  MANCHESTER,  June,  1844. 


James  Prescott  Joule  was  born  at  Manchester,  December 
24,  1818,  and  died  at  Sale,  his  country-place,  near  Manches- 
ter, October  11,  1889.  His  father  and  grandfather  were  brew- 
ers; and  he  himself  was  in  the  business  until  1854,  when  it 
was  sold.  He  was  sent  as  a  boy  to  learn  chemistry  from  Dai- 
ton,  and  became  so  interested  in  scientific  investigation  that 
his  father  furnished  a  laboratory  for  him  at  home.  The  re- 
searches described  in  the  preceding  paper  were  carried  out  in 
his  own  house  at  Oak  Field,  near  Manchester.  His  later  ex- 
periments were  performed  in  the  cellars  of  his  house  in  Acton 
Square,  Salford,  and  finally  in  a  large  yard  attached  to  the 
brewery,  New  Bailey  Street,  Salford. 

Among  the  most  important  of  his  researches  may  be  men- 
tioned : 

The  study  of  the  heating  effect  of  an  electric  current,  and  the 
discovery  of  the  law  HJ—^Rt,  which  bears  his  name.  (1840.) 

The  study  of  magnetization,  lifting-power,  saturation, changes 
of  dimension,  etc.  (1841,  1846.) 

The  experimental  verification  of  the  identity  of  various  forms 
of  energy.  (1843.) 

Various  researches  on  thermometry  and  measurement  of  tem- 
perature. He  accurately  determined  the  temperature  of  the 
maximum  density  of  water. 

A  series  of  important  experiments  on  gases.  He  was  the  first 
to  substitute  actual  values  in  Laplace's  corrected  formula  for 
the  velocity  of  sound. 

He  was  the  first  to  define  an  absolute  unit  for  electric  current; 
also  the  first  to  use  a  small  needle  in  a  tangent  galvanometer. 

The  memoirs  which  follow  contain  the  most  important  in- 
vestigations on  the  free  expansion  of  gases  carried  out  by  Joule 
himself  with  the  collaboration  of  Lord  Kelvin,  then  William 
Thomson. 

30 


Ox  THE  THERMAL  EFFECTS  OF  FLUIDS  IN  MOTION. 
BY  WILLIAM  THOMSON  AND  J.  P.  JOULE. 

PART      I.  Phil.  Trans.,  1853,  Vol.  CXLIIL,  p.  357  ;  (omitted) 

Abstract.     Proc.  Roy.  Soc.,  Vol.  VI.,  1853. 
PART    II.  Phil.  Trans.,  1854,  Vol.  CXLIV.,  p.  321; 

Abstract.  Proc.  Boy.  Soc.,  Vol.  VII.,  p.  127,  1854. 
PART  III.  Phil.   Trans.,  1860,  Vol.   CL.,   p.  325  ;    (omitted) 

Abstract.     Proc.  Roy.  Soc.,  Vol.  X.,  p.  519,  1860. 
PART  IV.  Phil.  Trans.,  1862,  Vol.  CLIL,  p.  579  ; 

Abstract.  Proc.  Roy.  Soc.,  Vol.  XII.,  p.  202,  1862. 

See  also  Joule's  Scientific  Papers,  Vol.  II.,  pp.  231-362; 
Thomson's  Mathematical  and  Physical  Papers,  Vol.  I.,  pp. 
346-455. 


CONTENTS 


PART  I. 

PAGE 

Expansion  through  a  Single  Aperture 33 

Expansion  through  Porous  Plugs 34 

PART  II. 

Apparatus 35 

Effect  of  Pressure  Variations 36 

Experiments  on  Air ;  Different  Plugs,  Pressures,  etc.    ...  39 

Experiments  on  Carbonic-Acid  Gas 40 

Experiments  on  Hydrogen 41 

Influence  of  Temperature  on  the  Cooling  Effect 44 

Theoretical  Deductions  : 
Section     I.    Work  Spent  in  Compressing  a  Gas  at  Constant 

Temperature 55 

Expansion  through  a  Porous  Plug     ....  57 

Discussion  of  Results 58 

Section    II.  Density  of  Saturated  Steam 64 

Section  III.  Emluation  of  Carnot's  Function 68 

Section  IV.  Absolute  Thermometric  Scale 73 

Comparison  with  Air-Thermometer     ....  76 
Section     V.  Physical  Properties  of  Air,  according  to  Abso- 
lute Scale  of  Temperature 76 

Abstract 83 

PART  IV. 

Discussion  of  Previous  Experiments 87 

New  Apparatus 89 

New  Experiments  on  Atmospheric  Air 92 

Experiments  on  Oxygen 92 

Experiments  on  Nitrogen .92 

New  Experiments  on  Carbonic  Acid 97 

New  Experiments  on  Hydrogen 97 

Discussion  of  Results 99 

Effect  of  Mixture  of  t7ie  Gases 99 

Abstract  .                        102 


ON  THE  THERMAL  EFFECTS  OF  ELASTIC  FLUIDS. 

BY  PROFESSOR  WILLIAM  THOMSON,  F.R.S.,  AND  J.  P.  JOULE, 

ESQ.,  F.R.S. 

(Abstract  of  the  preceding  paper.     [Part  /.]     Proceedings  Royal  Society, 

June  16,  1853.) 

THE  authors  had  already  proved,  by  experiments  conducted 
on  a  small  scale,  that  when  dry  atmospheric  air  exposed  to 
pressure  is  made  to  percolate  a  plug  of  non-conducting  porous 
material,  a  depression  of  temperature  takes  place,  increasing  in 
some  proportion  with  the  air  in  the  receiver.  The  numerous 
sources  of  error  which  were  to  be  apprehended  in  experiments 
of  this  kind,  conducted  on  a  small  scale,  induced  the  authors  to 
apply  for  the  means  of  executing  them  on  a  larger  scale  ;  and 
the  present  paper  contains  the  introductory  part  of  their  re- 
searches with  apparatus  furnished  by  the  Royal  Society,  com- 
prising a  force-pump  worked  by  a  steam-engine,  and  capable  of 
propelling  260  cubic  inches  of  air  per  second,  and  a  series  of 
tubes  by  which  the  elastic  fluid  is  conveyed  through  a  bath  of 
water,  by  which  its  temperature  is  regulated,  a  flange  at  the 
terminal  permitting  the  attachment  of  any  nozzle  which  is  de- 
sired. 

Preliminary  experiments  were  made  in  order  to  illustrate  the 
thermal  phenomena  which  result  from  the  rush  of  air  through 
a  single  aperture.  Two  effects  were  anticipated — one  of  heat, 
arising  from  the  vis  viva  of  air  in  rapid  motion  ;  the  other  of 
cold,  arising  from  dilatation  of  the  gas  and  the  consequent 
conversion  of  heat  into  mechanical  effect.  The  latter  was  ex- 
hibited by  placing  the  bulb  of  a  very  small  thermometer  close 
to  a  small  orifice  through  which  dry  atmospheric  air,  confined 
under  a  pressure  of  eight  atmospheres,  was  permitted  to  es- 
cape. In  this  case  the  thermometer  was  depressed  13°  Cent. 


FREE     EXPANSION     OF    GASES 

below  the  temperature  of  the  bath.  The  former  effect  was  ex- 
hibited by  causing  the  stream  of  air  as  it  issued  from  the  orifice 
to  pass  in  a  very  narrow  stream  between  the  bulb  of  the  ther- 
mometer and  a  piece  of  gutta-percha  tube  in  which  the  latter 
was  enclosed.  In  this  experiment,  with  a  pressure  of  eight  at- 
mospheres, an  elevation  of  temperature  equal  to  23°  Cent,  was 
observed.  The  same  phenomenon  was  even  more  strikingly 
exhibited  by  pinching  the  rushing  stream  with  the  finger  and 
thumb,  the  heat  resulting  therefrom  being  insupportable. 

The  varied  effects  thus  exhibited  in  the  "  rapids  "  neutralize 
one  another  at  a  short  distance  from  the  orifice,  leaving,  how- 
ever, a  small  cooling  effect,  to  ascertain  the  law  of  which  and 
its  amount  for  various  gases  the  present  researches  have  prin- 
cipally been  instituted.  A  plug  of  cotton  wool  was  employed 
for  the  purpose  at  once  of  preventing  the  escape  of  thermal  ef- 
fect in  the  rapids  and  of  mechanical  effect  in  the  shape  of 
sound.  With  this  arrangement  a  depression  of  0°.31  Cent,  was 
observed,  the  temperature  of  the  dry  atmospheric  air  in  the  re- 
ceiver being  14°. 5  Cent.,  and  its  pressure  34.4  Ibs.  on  the  square 
inch,  and  the  pressure  of  the  atmosphere  being  14.7  Ibs.  per 
square  inch. 


THE  THERMAL  EFFECTS  OF  FLUIDS  IN  MOTION. 


PART  II. 

BY  J.  P.  JOULE,  F.R.S.,  AND  PROFESSOR  W.  THOMSON,  M.A. 
F.R.S.*    (Phil.  Trans.,  1854,  Vol.  CXLIV.,  p.  321.) 

(Plates  I.  and  II.) 

IN  the  last  experiment  re- 
lated in  our  former  paper, f  in 
which  a  low  pressure  of  air  was 
employed,  a  considerable  vari- 
ation of  the  cooling  effect  was 
observed,  which  it  was  neces- 
sary to  account  for  in  order  to 
ascertain  its  influence  on  the 
results.  We  therefore  contin- 
ued the  experiments  at  low 
pressure,  trying  the  various 
arrangements  which  might  be 
supposed  to  exercise  influence 
over  the  phenomena.  We  had 
already  interposed  a  plug  of 
cotton-wool  between  the  iron 
and  copper  pipes,  which  was 
found  to  have  the  very  impor- 
tant effect  of  equalizing  the 
pressure,  besides  stopping  any 
solid  or  liquid  particles  driven 
from  the  pump,  and  which  has 
therefore  been  retained  in  all 
the  subsequent  experiments. 
Another  improvement  was  now 
effected  by  introducing  a  noz- 

*  The  experiments  were  made  at  the   Salford  Brewery,  New   Bailey 
Street,  t  Phil.  Trans.,  1853,  Part  III 

35 


MEMOIRS    ON    THE 

zle  constructed  of  boxwood,  instead  of  the  brass  one  previously 
used.  This  nozzle  is  represented  by  Fig.  1,  Plate  1,  in  which 
a  a  is  a  brass  casting  which  bolts  upon  the  terminal  flange  of 
the  copper  piping;  1}  1)  is  a  turned  piece  of  boxwood  screwing 
into  the  above,  having  two  ledges  for  the  reception  of  perfo- 
rated brass  plates,  the  upper  plate  being  secured  in  its  place 
by  the  turned  boxwood  c  c,  which  is  screwed  into  the  top  of 
the  first  piece. 

The  space  enclosed  by  the  perforated  plates  is  2.72  inches 
long,  and  an  inch  and  a  half  in  diameter,  and  being  filled  with 
cotton,  silk,  or  other  material  more  or  less  compressed,  pre- 
sents as  much  resistance  to  the  passage  of  the  air  as  may  be  de- 
sired. A  tin  can,  d,  filled  with  cotton  -  wool,  and  screwing  to 
the  brass  casting,  serves  to  keep  the  water  of  the  bath  from 
coming  in  contact  with  the  boxwood  nozzle. 

In  the  following  experiments,  made  in  order  to  ascertain  the 
variations  in  the  cooling  effect  above  referred  to,  the  nozzle 
was  filled  with  382  grs.  of  cotton-wool,  which  was  sufficient 
to  keep  up  a  pressure  of  about  34  Ibs.  on  the  inch  in  the  tubes 
when  the  pump  was  working  at  the  ordinary  rate.  By  open- 
ing the  stopcock  in  the  main  pipe  this  pressure  could  be 
further  reduced  to  about  22  Ibs.  by  diminishing  the  quantity 
of  air  arriving  at  the  nozzle.  By  shutting  and  opening  the 
stopcock,  we  had  therefore  the  means  of  producing  a  tempo- 
rary variation  of  pressure,  and  of  investigating  its  effect  on  the 
temperature  of  the  air  issuing  from  the  nozzle.  In  the  first 
experiments  the  stopcock  was  kept  open  for  a  length  of  time, 
until  the  temperature  of  the  rushing  air  became  pretty  con- 
stant ;  it  was  then  shut  for  a  period  of  3f ,  7£,  15,  30,  or  60 
seconds,  then  reopened.  The  oscillations  of  temperature  thus 
produced  are  laid  down  upon  the  Chart  No.  1,  in  which  the 
ordinates  of  the  curves  represent  the  temperatures  according 
to  the  scale  of  thermometer  C,  each  division  corresponding  to 
0.0477  of  a  degree  Centigrade.  The  divisions  of  the  horizon- 
tal lines  represent  intervals  of  time  equal  to  a  quarter  of  a  min- 
ute. The  horizontal  black  lines  show  the  temperature  of  the 
bath  in  each  experiment.  [Chart  is  omitted.'] 

The  effect  upon  the  pressure  of  the  air  produced  by  shutting 
the  stopcock  during  various  intervals  of  times,  is  given  in  the 
following  table  : 

36 


FREE     EXPANSION     OF    GASES 


Stopcock  Shut  for 

5  8. 

15  s. 

30s. 

1  m. 

2m.     , 

M.         S. 

Initial  pressure 

22  35 

22  35 

22  35 

22  35 

22  35 

Pressure  after  ...             05 

24  92 

2492 

24  92 

24  92 

24  92 

Pressure  after  0    15 

23.07 

28.46 

28  46 

28  46 

28  46 

Pressure  after                      0    30 

22  43 

23  38 

30  84 

30  84 

30  84 

Pressure  after  G     45 

22  35 

22  5 

24  27 

32  03 

32  03 

Pressure  after                      1      0 

22  35 

22  43 

22  83 

32  79 

32  79 

Pressure  after  1     15 
Pressure  after  1     30 

22.35 
22  35 

22.45 
22  35 

24.54 
22  83 

33.08 
38  25 

Pressure  after                      1     45 

22  35 

22  43 

33  33 

Pressure  after         2      0 

22  35 

33  41 

Pressure  after                      2    15 

22  35 

24  54 

Pressure  after             ...  2    30 

22  54 

Pressure  after  2    45 

22  40 

Pressure  after  3      0 

22  35 

The  last  column  gives  also  the  effect  occasioned  by  the  per- 
manent shutting  or  opening  of  the  stopcock,  33.41  Ibs.  being 
nearly  equal  to  the  pressure  when  the  stopcock  has  been  closed 
for  a  long  time. 

In  the  next  experiments,  the  opposite  effect  of  opening  the 
stopcock  was  tried,  the  results  of  which  are  laid  down  on 
Chart  No.  2.  [Chart  is  omitted.] 

The  effect  upon  the  pressure  of  the  air  produced  by  opening 
the  stopcock  during  the  various  intervals  of  time  employed  in 
the  experiments  is  exhibited  in  the  next  table  : 


Stopcock  Opened  for 

Si  s. 

74  *• 

15s. 

30  s. 

I  m. 

M.         S. 

Initial  pressure 

34  37 

34  37 

34  37 

34  37 

34  37 

Pressure  after  0      3f 
Pressure  after  0      7£ 

29.57 

29.57 
27.43 

29.57 
27.43 

29.57 
27.43 

29.57 

27  43 

Pressure  after  0     15 

32.47 

30.41 

25.15 

25.15 

25.15 

Pressure  after  .    .            0    30 

33  5 

32  47 

30  41 

23.23 

23  23 

Pressure  after  0    45 

33.94 

33.5 

32.4 

29.4 

22  9 

Pressure  after                  1      0 

34  1 

34  1 

33  5 

32.13 

22  76 

Pressure  after  ....          1     15 

34  2 

34.3 

33.94 

33.24 

28  82 

Pressure  after                  1     30 

34  33 

34  37 

34  14 

33  90 

31  44 

Pressure  after  1    45 

34.37 

34.37 

34  30 

34.14 

32  9 

Pressure  after  2      0 
Pressure  after  2    15 
Pressure  after  2    30 

34.37 

34.33 
34.37 

33.66 
34.06 
34.20 

Pressure  after                  2    45 

34  37 

MEMOIRS     ON     THE 

The  remarkable  fluctuations  of  temperature  in  the  issuing 
stream  accompanying  such  changes  of  pressure,  and  continu- 
ing to  be  very  perceptible  in  the  different  cases  for  periods  of 
from  three  to  four  minutes  up  to  nearly  half  an  hour  after  the 
pressure  had  become  sensibly  uniform,  depend  on  a  complica- 
tion of  circumstances,  which  appear  to  consist  of  (1)  the  change 
of  cooling  effect  due  to  the  instantaneous  change  of  pressure  ; 
(2)  a  heating  or  cooling  effect  produced  instantaneously  by 
compression  or  expansion  in  all  the  air  flowing  towards  and  en- 
tering the  plug,  and  conveyed  through  the  plug  to  the  issuing 
stream ;  and  (3)  heat  or  cold  communicated  by  contact  from 
the  air  on  the  high-pressure  side  to  the  metals  and  boxwood, 
and  conducted  through  them  to  the  issuing  stream. 

The  first  of  these  causes  may  be  expected  to  influence  the  is- 
suing stream  instantaneously  on  any  change  in  the  stopcock  ; 
and  after  fluctuations  from  other  sources  have  ceased  it  must 
leave  a  permanent  effect  in  those  cases  in  which  the  stopcock 
is  permanently  changed.  But  after  a  certain  interval  the  re- 
verse agency  of  the  second  cause,  much  more  considerable  in 
amount,  will  begin  to  affect  the  issuing  stream,  which  will  soon 
preponderate  over  the  first,  and  (always  on  the  supposition  that 
this  conviction  is  uninfluenced  by  conduction  of  any  of  the 
materials)  will  affect  it  with  all  the  variations,  undiminished  in 
amount,  which  the  air  entering  the  plug  experiences,  but  be- 
hind time  by  a  constant  interval  equal  to  the  time  occupied  by 
as  much  air  as  is  equal  in  thermal  capacity  to  the  cotton  of  the 
plug  in  passing  through  the  apparatus.  This,  in  the  experi- 
ments with  the  stopcock  shut,  would  be  very  exactly  a  quarter 
of  a  minute;  but  it  appears  to  have  averaged  more  nearly  one- 
third  of  a  minute  in  the  varying  circumstances  of  the  actual 
experiments,  since  our  observations  (as  maybe  partially  judged 
from  the  preceding  charts)  showed  us,  with  very  remarkable 
sharpness,  in  each  case  about  twenty  seconds  after  the  shutting 
or  opening  of  the  stopcock,  the  commencement  of  the  heating 
or  cooling  effect  on  the  issuing  stream,  due  to  the  sudden  com- 
pression or  rarefaction  instantaneously  produced  in  the  air  on 
the  other  side  of  the  plug. 

The  entering  air  will,  very  soon  after  its  pressure  ceases  to 
vary,  be  reduced  to  the  temperature  of  the  bath  by  the  excel- 
lent conducting  action  of  the  spiral  copper  pipe  through  which 
it  passes ;  and,  consequently,  twenty  seconds  or  so  later,  the 


FREE     EXPANSION     OF    GASES 

issuing  stream  can  experience  no  further  fluctuations  in  tem- 
perature except  by  the  agency  depending  on  the  third  cause. 

That  the  third  cause  may  produce  very  considerable  effects 
is  obvious,  when  we  think  how  great  the  variations  of  temper- 
ature must  be  to  which  the  surface  of  the  solid  materials  in  the 
neighborhood  of  the  plug  on  the  high-pressure  side  are  sub- 
jected during  the  sudden  changes  of  pressure,  and  that  the 
heat  consequently  taken  in  or  emitted  by  these  bodies  may  in- 
fluence the  issuing  stream  perceptibly  for  a  quarter  or  a  half 
hour  after  the  changes  of  pressure  from  which  it  originated 
have  ceased,  is  quite  intelligible  on  account  of  the  slowness  of 
conduction  of  heat  through  the  wood  and  metals,  when  we  take 
into  account  the  actual  dimensions  of  the  parts  of  the  appara- 
tus round  the  plug.  It  is  not  easy,  however,  to  explain  all  the 
fluctuations  of  temperature  which  have  been  observed  after  the 
pressure  had  become  constant  in  the  different  cases.  Those  shown 
in  the  first  set  of  diagrams  are  just  such  as  might  be  expected 
from  the  alternate  heating  and  cooling  which  the  solids  must 
have  experienced  at  their  surfaces  on  the  high  -  pressure  side, 
and  which  must  be  conducted  through  so  as  to  affect  the  issu- 
ing stream  after  a  considerable  time ;  but  the  great  elevations 
of  temperature  shown  in  the  second  set  of  diagrams,  which  cor- 
respond to  cases  when  the  pressure  was  temporarily  or  perma- 
nently diminished,  are  not,  so  far  as  we  see,  explained  by  the 
causes  we  have  mentioned,  and  the  circumstances  of  these  cases 
require  further  examination. 

When  we  had  thus  examined  the  causes  of  the  fluctuations  of 
temperature  in  the  issuing  air,  the  precautions  to  prevent  their 
injurious  effect  upon  the  accuracy  of  the  determinations  of  the 
cooling  effect  in  the  passage  of  air  through  the  porous  plug  be- 
came evident.  These  were  simply  to  render  the  action  of  the 
pump  as  uniform  as  possible,  and  to  commence  the  record  of 
observations  only  after  one  hour  and  a  half  or  two  hours  had 
elapsed  from  the  starting  of  the  pump.  The  system  then 
adopted  was  to  observe  the  thermometers  in  the  bath  and 
stream  of  air,  and  the  pressure-gauge  every  two  minutes  or 
minute  and  a  half  ;  the  means  of  which  observations  are  re- 
corded in  the  columns  of  the  tables.  In  some  instances  the  air, 
previous  to  passing  into  the  pump,  was  transmitted  through  a 
cylinder  which  had  been  filled  with  quick-lime.  But  since  by 
previous  use  its  power  of  absorbing  water  had  been  consider- 

39 


MEMOIRS    ON    THE 

ably  deteriorated,  a  portion  of  the  air  was  always  transmitted 
through  a  Liebig  tube  containing  asbestos  moistened  with  sul- 
phuric acid  or  chloride  of  zinc.  The  influence  of  a  small  quan- 
tity of  moisture  in  the  air  is  trifling.,  but  will  hereafter  be  exam- 
ined. That  of  the  carbonic  acid  contained  by  the  atmosphere 
was,  as  will  appear  in  the  sequel,  quite  inappreciable.  It  will 
be  proper  to  observe  that  the  thermometers,  by  which  the  tem- 
perature of  the  bath  and  issuing  air  was  ascertained,  were  re- 
peatedly compared  together  to  avoid  any  error  which  might 
arise  from  the  alteration  of  their  fixed  points  from  time  to 
time. 

In  each,  excepting  the  first  of  the  seven  experiments  record- 
ed, the  air  passed  through  the  quick-lime  cylinder. 


TABLE  I. 

Experiments  with  a  plug  consisting  of  191  grains  of  cotton -wool. 


1 

2 

3 

4 

5 

6 

7 

8 

No.  of  Obser- 

vations from 
which  the 
Results  in 
Columns  4, 
6,  and  7  are 

Cu.  In. 

passed 
through 
Nozzle  per 
Min. 

Water  in 
100  Grains 
of  Air,  in 
Grajns 

Pressure 
in  Lbs.  on 
the  Square 
Inch 

Atmos- 
pheric 
Pressure 

Tempera- 
ture of  the 
Bath 

Tempera- 
ture of  the 
Issuing  Air 

Cooling 
Effect 
in  Cent. 
Degrees 

Obtained 

20 

10822 

0.51 

21.326 

14.400 

20.295 

20.201 

0.094 

20 

10998 

0.30 

21.239 

14.252 

16.740 

16.615 

0.125 

10 

Not  obsv'd 

0.56 

20.446 

14609 

17.738 

17.622 

0.116 

10 

10769 

0.66 

20.910 

14.772 

16.039 

15.924 

0.115 

10 

10769 

0.66 

20.934 

14.775 

16.065 

15.967 

0.098 

10 

10769 

0.66 

20.995 

14.779 

16.084 

15.984 

0.100 

10 

10769 

0.66 

20.933 

14.782 

16.081 

15.974 

0.107 

Mean 

057 

20969 

14.624 

17.006 

16.898 

0.108 

In  the  next  experiments  the  nozzle  was  filled  with  382  grains 
of  cotton  -  wool.  The  intermediate  stopcock,  however,  was 
partly  opened,  in  order  that  by  discharging  a  portion  of  air 
before  its  arrival  at  the  nozzle  the  pressure  might  not  be  widely 
different  from  that  employed  in  the  last  series.  In  all,  except- 
ing the  last  experiment  recorded  in  the  following  table,  the 
cylinder  of  lime  was  dispensed  with. 

40 


FREE    EXPANSION    OF    GASES 


TABLE  II. 

Experiments  with  a  smaller  quantity  of  air  passed  through  a  plug  consist- 
ing of  382  grs.  of  cotton-wool. 


1 

2 

3 

4 

5 

6 

7 

8 

No.  of  Obser- 

vations from 
which  the 
Results  in 
Columns  4, 
6,  and  7  are 

Cu.  In. 
passed 
through 
Nozzle  per 
Mm. 

Water  in 
100  Grains 
of  Air,  in 
Grains 

Pressure 
in  Lbs.  on 
the  Square 
Inch 

Atmos- 
pheric 
Pressure 

Tempera- 
ture of  the 
Bath 

Tempera- 
ture of  the 
Issuing  Air 

Cooling 
Effect 
in  Cent. 
Degrees 

Obtained 

0 

0 

o 

Mean 

0  90 

22.678 

14.540 

20.125 

19.979 

0.146 

TABLE  III. 

Experiments  in  which  the  entire  quantity  of  air  propelled  by  the  pump 

was  passed  through  a  plug  consisting  of  382  grains  of  cotton-wool. 

The  cylinder  of  lime  was  not  employed. 


1 

2 

3 

4 

5 

6 

7 

8 

No.  of  Obser- 

vations from 
which  the 
Results  in 
Columns  4, 
6,  and  7  are 

Cu.  In. 
passed 
through 
Nozzle  per 
Min. 

Water  in 
100  Grains 
of  Air,  in 
Grains 

Pressure 
in  Lbs.  on 
the  Square 
Inch 

Atmos- 
pheric 
Pressure 

Tempera- 
ture of  the 
Bath 

Tempera- 
ture of  the 
Issuing  Air 

Cooling 
Effect 
in  Cent. 
Degrees 

Obtained 

7 

11766 

0.56 

36625 

14.583 

1°9  869 

19.535 

0.334 

10 

Not  obsv'd 

0.56 

35.671 

14.790 

20.419 

20.098 

0.321 

10 

"      " 

0.36 

35.772 

14.504 

16.096 

15.730 

0.366 

10 

it      « 

0.36 

35.872 

14.504 

16.104 

15.721 

0.383 

10 

11      <  < 

0.36 

36.026 

14.504 

16.232 

15.869 

0.363 

Mean 

044 

35  993 

14577 

17.744 

17390 

0.354 

In  the  next  series  of  experiments  the  air  was  passed  through 
a  plug  of  silk,  formed  by  rolling  a  silk  handkerchief  into  a 
cylindrical  shape,  and  then  screwing  it  into  the  nozzle.  The 
silk  weighed  580  grains,  and  the  small  quantity  of  cotton-wool 
placed  on  the  side  next  the  thermometer,  in  order  to  equalize 
the  stream  of  air  more  completely,  weighed  15  grains.  The 
stopcock  was  partly  opened,  as  in  the  experiments  of  Table  II., 
in  order  to  reduce  the  pressure  to  that  obtained  by  passing  the 
full  quantity  of  air  propelled  by  the  pump  through  a  more 
porous  plug.  The  cylinder  of  lime  was  employed. 

41 


MEMOIRS    ON    THE 


TABLE  IV. 

Experiments  in  which  a  smaller  quantity  of  air  was  passed  through  a  plug 
consisting  of  580  grains  of  silk. 


1 

2 

3 

4 

5 

6 

7 

8 

No.  of  Obser- 

vations from 
which  the 
Results  in 
Columns  4, 
6,  and  7  are 

Cu.  In. 
p;issed 
through 
Nozzle  per 
Min. 

Water  in 
100  Grains 
of  Air,  in 
Grains 

Pressure 
in  Lbs.  on 
the  Square 
Inch 

Atmos- 
pheric 
Pressure 

Tempera- 
ture of  the 
Bath 

Tempera- 
ture of  the 
Issuing  Air 

Cooling 
Effect 
in  Cent. 
Degrees 

Obtained 

0 

o 

0 

Mean 



0.16 

33.809 

14.692 

18.975 

18.610 

0.365 

TABLE  V. 

Experiments  in  which  the  entire  quantity  of  air  propelled  by  the  pump 
was  passed  through  the  silk  plug.     The  cylinder  of  lime  was  em- 
ployed in  all  excepting  the  first  two  experiments. 


1 

2 

3 

4 

5 

6 

7 

3 

No.  of  Obser- 

vations from 
which  the 
Results  in 
Columns  4, 
6,  and  7  are 

Cu.  In. 
passed 
through 
Nozzle  per 
Min. 

Water  in 
100  Grains 
of  Air,  in 
Grains 

Pressure 
in  Lbs.  on 

the  Square 
Inch 

Atmos- 
pheric 
Pressure 

Tempera- 
ture of  the 
Bath 

Tempera- 
ture of  the 
Issuing  Air 

Cooling 
Effect 
in  Cent. 
Degrees 

Obtained 

0 

0 

o 

Mean 

0.23 

54456 

14.591 

17  809 

17  102 

0  707 

In  order  to  obtain  a  greater  pressure,  a  ping  was  formed  of 
silk  "  waste  "  compressed  very  tightly  into  the  nozzle. 


TABLE  VI. 

Experiments  in  which  the  air,  after  passing  through  the  cylinder  of  lime, 
was  forced  through  a  plug  consisting  of  740  grains  of  silk. 


1 

2 

3 

4 

5 

6 

7 

8 

No.  of  Obser- 

vations from 
which  the 
Results  in 
Columns  4, 
6.  and  7  are 

Cu.  In. 

passed 
through 
Nozzle  per 
Min. 

Water  in 
100  Grains 
of  Air,  in 
Grains 

Pressure 
in  Lbs.  on 
the  Square 
Inch 

Atmos- 
pheric 
Pressure 

Tempera- 
ture of  the 
Bath 

Tempera- 
ture of  the 

Issuing  Air 

Cooling 
Effect 
in  Cent. 
Degrees 

Obtained 

0 

0 

0 

Mean 

0.16 

79.250 

14.793 

15.483 

14373 

1.110 

FREE     EXPANSION     OF     GASES 


In  the  foregoing  experiments  the  pressure  of  the  air  on  its 
exit  from  the  plug  was  always  exactly  equal  to  the  atmospheric 
pressure.  To  ascertain  the  effect  of  an  alteration  in  the  press- 
ure of  the  exit  air,  we  now  enclosed  a  long  siphon  barometer 
within  the  glass  tube  (Fig.  14).  The  upper  part  of  this  tube 
was  surmounted  with  a  cap,  furnished  with  a  stopcock,  by 
partially  closing  which  the  air  at  its  exit  could  be  brought  to 
the  required  pressure.  The  influence  of  pressure  in  raising  the 
mercury  in  the  thermometer  by  compressing  its  bulb  was  ascer- 
tained by  plunging  the  instrument  into  a  bottle  of  water  within 
the  glass  tube,  and  noting  the  amount  of  the  sudden  rise  or  fall 
of  the  quicksilver  on  a  sudden  augmentation  or  reduction  of 
pressure.  It  was  found  that  the  pressure,  equal  to  that  of  17 
inches  of  mercury,  raised  the  indication  by  0°.09,  which  quan- 
tity was  therefore  subtracted  after  the  usual  reduction  of  the 
thermometric  scale. 


TABLE  VII. 

Experiments  with  the  plug  consisting  of  740  grains  of  silk, 
the  exit  air  increased.     Cylinder  of  lime  used. 


Pressure  of 


1 

2 

3 

4 

5 

6 

7 

8 

Xo.  of  Obser- 

vations from 
which  the 
Results  in 
Columns  4, 
fi,  and  7  are 

Cu.  In. 
passed 
through 
Nozzle  per 
Min. 

Water  in 
100  Grains 
of  Air,  in 
Grains 

Pressure 
in  Lbs.  on 
the  Square 
Inch 

Atmos- 
pheric 
Pressure 

Tempera- 
ture of  the 
Bath 

Tempera- 
ture of  the 
Issuing  Air 

Cooling 
Effect 
in  Cent. 
Degrees 

Obtained 

Mean 

Estimated 
at  5400 

0.14 

82.004 

22.814 

12.734 

11.701 

1.033 

With  reference  to  the  experiments  in  Table  VII. ,  it  may  be 
remarked  that  the  cooling  effect  must  be  the  excess  of  that 
which  would  have  been  obtained  had  the  air  been  only  resisted 
by  the  atmospheric  pressure  in  escaping  from  the  plug,  above 
the  cooling  effect  that  would  be  found  in  an  experiment  with 
the  temperature  of  the  bath  and  the  pressure  of  the  entering 
air  the  same  as  the  temperature  and  pressure  of  the  exit  air  in 
the  actual  experiment,  and  the  air  issuing  at  atmospheric  press- 
ure. Hence,  since  two  or  three  degrees  of  difference  of  tem- 
perature in  the  bath  would  not  sensibly  alter  the  cooling  effect 
in  any  of  the  experiments  on  air,  the  cooling  effect  in  an  experi- 

43 


MEMOIRS     ON     THE 

ment  in  which  the  pressure  of  the  exit  air  is  increased  must 
be  sensibly  equal  to  the  difference  of  the  cooling  effects  in  two 
of  the  ordinary  experiments,  with  the  high  pressures  the  same 
as  those  used  for  the  entering  and  issuing  air  respectively,  and 
the  low  pressure  that  of  the  atmosphere  in  each  case  ;  a  conclu- 
sion which  is  verified  by  the  actual  results,  as  the  comparison 
given  below  shows. 

The  results  recorded  in  the  foregoing  tables  are  laid  down  on 
Chart  No.  3,  in  which  the  horizontal  lines  represent  the  excess  of 
the  pressure  of  the  air  in  the  receiver  over  that  of  the  exit  air  as 
found  by  subtracting  the  fifth  from  the  fourth  columns  of  the 
tables,  and  the  vertical  lines  represent  the  cooling  effects  in 
tenths  of  a  degree  Centigrade.  It  will  be  remarked  that  the 
line  drawn  through  the  points  of  observation  is  nearly  straight, 
indicating  that  the  cooling  effect  is,  approximately  at  least, 
proportional  to  the  excess  of  pressure,  being  about  .018°  per 
pound  on  the  square  inch  of  difference  of  pressure.  Or  we 
may  arrive  at  the  same  conclusion  by  dividing  the  cooling 
effect  (e>)  by  the  difference  of  pressure  (P—  P')  in  the  different 
experiments.  We  thus  find,  from  the  means  shown  in  the  dif- 
ferent tables  : 


-i-cauio  I  A«  1 

p  p/  ~ 

(II.) 

.0179 

(III.) 

.0105 

(IV.) 

.0106 

(V.) 

.0177 

(VI.) 

.0172 

(VII.) 

.0174 

Mean, 

.0176 

On  the  Cooling  Effects  Experienced  ~by  Carbonic  Acid  in 
Passing  TJirough  a  Porous  Plug. 

The  position  of  the  apparatus  gave  us  considerable  practical 
facilities  in  experimenting  with  carbonic  acid.  A  fermenting 
tun,  10  feet  deep  and  8  feet  square,  was  filled  with  wort  to  a 
depth  of  6  feet.  After  the  fermentation  had  been  carried  on 
for  about  forty  hours,  the  gas  was  found  to  be  produced  in 
sufficient  quantity  to  supply  the  pump  for  the  requisite  time. 
The  carbonic  acid  was  conveyed  by  a  gutta-percha  pipe  and 

44 


FREE     EXPANSION    OF    GASES 

passed  through  two  glass  vessels  surrounded  by  ice  in  order  to 
condense  the  greater  portion  of  vapors.  In  the  succeeding 
experiment  the  total  quantity  of  liquid  so  condensed  was  300 
grains,  which,  having  a  specific  gravity  of  .9965,  was  composed 
of  10  grains  of  alcohol  and  290  grains  of  water.  On  analyzing 
a  portion  of  the  gas  during  the  experiment  by  passing  it 
through  a  tube  containing  chloride  of  zinc,  it  was  found  to 
contain  0.733  grain  of  water  to  100  grains  of  carbonic  acid. 

In  Table  IX.,  as  well  as  in  the  next  series,  the  carbonic  acid 
contained  0.35  per  cent,  of  water. 

In  the  experiment  of  Table  X.,  as  well  as  in  those  of  the 
adjoining  tables,  the  sudden  diminution  of  pressure  on  con- 
necting the  pump  with  the  receiver  containing  carbonic  acid, 
is  in  perfect  accordance  with  the  discovery  of  Prof.  Graham 
of  the  superior  facility  with  which  that  gas  may  be  transmitted 
through  a  porous  body  compared  with  an  equal  volume  of  at- 
mospheric air. 


MEMOIRS    ON    THE 


TABLE  VIII. 

Carbonic  acid  forced  through  a  plug  of  382  grs.  of  cotton -wool.     Mean 
barometric  pressure,  29.45  inches,  equivalent  to  14.399  Ibs.     Gauge 
under  atmospheric  pressure,  151.     The  pump  was  placed  in  con- 
nection with  the  pipe  immersed  in  carbonic  acid  at  10h-  55m- 


Time  of 
Observa- 
tion 

Vol.  Percentage 
of  Carbonic  Acid 

Pressure  Gauge  ;  Mean 
Pressure  in  Lbs.  on  the 
Square  Inch 

Temperature  of  the 
Bath  by  Indications 
of  Thermometer 

Temperature  of  the 
Issuing  Gas  by 
Indications  of 
Thermometer 

Cooling  Ef- 
fect in  Cent. 
Degrees 

h.      m. 

10     47 

0 

79.0 

486.0 

49 
53 

0 
0 

79.0 
79.6 

486.0 

57 

85.2 

58 

86.0 

59 

85.0 

188  6 

11       0 
2 

85.0 
86.4 

188^5 

4 

86.7 

6 

86.6 

9 

95.51 

86.6 

13 

84.0 

14 

84.2 

Ibs. 

15 
19 

95.51 

-94.89 

84.4 
84.5 

•  84.906  =  32.989 

486.00  =  200.001 

188.36  =  18°.611 

1°.390 

22 

84.1 

24 

84.6 

25 

93.03 

84.2 

28 

84.1 

32 

1 

83.2 

33 

83.8' 

35 

86.82 

84.0 

40 

83.8 

41 

83.9 

43 

85.0  j 

45 

79.37 

80.61 

86.0 

84.  245  =  32.  286  1485.  94  =  19°.  998 

190.1  =  18°.787 

jo  211 

49 

84.6 

51 

84.5 

53 

83.9 

55 

75.65 

3.6 

12      0 

3.6 

2 

3.0 

5 

70.68 

2.7 

9 

(68.82 

2.7 

82.783  =  33.960 

485.52  =  19°.980 

91.07  =  180.884 

1°.096 

13 

82.9 

15 

82.7 

21 

82.7 

23 

82.8  ' 

25 

65.72 

82.9 

28 

82.9 

33 

32.2 

35 

63.23 

32.3 

40 

31.9 

44 

31.9 

45 

63.23  J.63.85 

32.1 

82.986  =  33.864 

185.18  =  190.966 

191.82  =  18°.  959 

1°.007 

52 

32.4 

55 

62.0 

^3.9 

2 

34!l 

5 

63.23 

34.9 

11 

*5.4 

15 

65.72 

32.1 

FREE    EXPANSION    OF    GASES 


TABLE   IX. 

Carbonic  acid  forced  through  a  plug  consisting  of  191  grs.  of  cotton-wool. 
Mean   barometric    pressure,    29.6   inches,  equivalent   to   14.472  Ibs. 
Gauge  under  atmospheric  pressure,  150.6.     Pump  placed  in  con- 
nection with  the  pipe  immersed  in  carbonic  acid  at  10h-  88m- 


1 

2 

3 

4 

5 

6 

Time  of 
Observa- 
tion 

Vol.  Percentage 
ot  Carbonic  Acid 

Pressure  Gauge  and  Pressure 
in  Lbs.  on  the  Square  Inch 
Equivalent  Thereto 

Indication  of  Ther- 
mometer. Tempera- 
ture of  the  Bath 

Indication  of  Ther- 
mometer. Tempera- 
ture of  the  Issuing 
Gas 

Cooling  Ef- 
fect in  Cent. 
Degrees 

h.      m. 

10     40 

42 

44 

1 

50 

95.51 

53 

55 

Ibs. 

57 

Y  94.58 

122.91  =  20.43 

461.78  =  18°.962 

187.  49  =  18°.  522 

0°.44 

59 

11      0 

93.65 

1 

3 

5 

•t 

7 

9 
10 

81.  8G 

11 

15 

•  76.27 

121.91  =  20.682 

462.  11  =  18°.  976 

188.  35  =  18°.  609 

0°.367 

17 

19 

20 

70.  G8 

21 

25  '             J 

MEMOIRS    ON    THE 


TABLE  X. 

Experiment  in  which  carbonic  acid  was  forced  through  a  plug  consisting 

of  580  grs.  of  silk.     Mean  barometric  pressure,  29.56,  equivalent  to 

14.452  Ibs.     Gauge  under  atmospheric  pressure,  150.8.     Pump 

placed  in  connection  with  the  pipe  immersed  in   carbonic 

acid  at  12h-  53m-.     Quantity  of  gas  forced  through  the 

plug,  about  7170  cubic  inches  per  minute. 


1 

2 

3 

4 

5 

6 

Time  of 
Observa- 
tion 

Vol.  Percentage 
of  Carbonic  Acid 

Pressure  Gaujre  and  Pressure 
iu  Lbs.  on  the  Square  Inch 
Equivalent  Thereto 

Indication  of  Ther- 
mometer. Tempera- 
ture of  the  Bath 

Indication  of  Ther- 
mometer.    Tempera- 
ture of  the  Issuing 
Gas 

Cooling  Ef- 
fect in  Cent. 
Degrees 

h.      m. 
12     42 

44 
46 

0 

Ibs. 
52.2  =  55.454 

464  34  —  19O  072 

185.  53  =  ISO.  323 

0°.740 

49 

0 

50 

0 

52 

0 

54 

57 

1      0 

95.51  1 

5 

7 

| 

9 
10 

96.00  ;>94.8.-> 

55.92  =  51.7 

464.  47  =  19°.  077 

165.0  =  16°.256 

2°.  821 

11 

13 

17 

1 

20 

93.03  J 

24 

25 

27 

30 

85.02 

55.94=51.68 

464.  71  =  19°.  088 

167.  8  =  10°.  538 

2°.  550 

35 

30 

38 

FREE     EXPANSION     OF    GASES 


TABLE  XI. 

Experiment  in  which  carbonic  acid  was  forced  through  a  plug  consisting 

of  740  grs.  of  silk.     Mean  barometric  pressure,  30.065,  equivalent  to 

14.723  Ibs.  on   the  inch.      Gauge  under  atmospheric   pressure 

145.65.     Pump  placed  in  connection  with  the  pipe  immersed 

in  carbonic  acid  nt  llh-  37m-.     Percentage  of  moisture  in 

the  carbonic  acid,  0.15. 


1 

2 

3 

4 

5 

6 

Time  of 
Observa- 
tion 

Vol.  Percentage 
of  Carbonic  Acid 

Pressure  Gua*e  and  Pressure 
in  Lbs.  on  the  Square  Inch 
Equivalent  Thereto 

Indication  of  Ther- 
mometer. Tempera- 
ture of  the  Bath 

Indication  of  Ther- 
mometer. Tempera- 
ture of  the  Issuing 
Gag 

Cooling  Ef- 
fect in  Cent. 
Degrees 

h.      m. 

11     28 

35.5 

30 

35.1 

32 

35.6 

34 

35.2 

36 

35.2 

37 

36.0 

38 

36.2 

3!> 

95.51 

36.6 

43 

36.9 

45 

95.51 

37.0 

47 

37.1 

50 

95.51  I 

37.0 

53 

j 

37.0 

55 

95.51  | 

37.0 

Ibs. 

57 

V  95.51 

3T.O 

37.0  =  75.324 

319.  17  =12°.  844 

82.  02  =  7°.  974 

4°.  87 

12      0 

95.51  1 

37.0 

2 

37.0 

5 

95.51  J 

37.0 

In  order  to  ascertain  the  cooling  effect  due  to  pure  carbonic 
acid,  we  may  at  present  neglect  the  effect  due  to  the  small 
quantity  of  watery  vapor  contained  by  the  gas ;  and  as  the  cool- 
ing effects  observed  in  the  various  mixtures  of  atmospheric  air 
and  carbonic  acid  appear  nearly  consistent  with  the  hypothesis 
that  the  specific  heats  of  the  two  elastic  fluids  are  for  equal 
volumes  equal  to  one  another,  and  that  each  fluid  experiences 
in  the  mixture  the  same  thermo-dynamic  effect  as  if  the  other 
were  removed,  we  may  for  the  present  take  the  following  esti- 
mate of  the  cooling  effects  due  to  pure  carbonic  acid,  at  the 
various  temperatures  and  pressures  employed,  calculated  by 
means  of  this  hypothesis  from  the  observations  in  which  the 
percentage  of  carbonic  acid  was  the  greatest,  and,  in  fact,  so 
great  that  a  considerable  error  in  the  correction  for  the  com- 
mon air  would  scarcely  affect  the  result  to  any  sensible  extent. 
D  49 


MEMOIRS     ON     THE 


Temperature  of 
the  Bath 

Excess  of  Press- 
ure P-P' 

Cooling  Effect 

i 

Cooling  Effect 
Divided  by  Excess 
of  Pressure 

From  Table     IX. 
From  Table  VIII. 
From  Table       X. 
From  Table     XI. 

18.962 
20.001 
19.077 
12.844 

5.958 
18.590 
37.248 
60.601 

0.459 
1.446 
2.938 
5.049 

.0770 
.0778 
.0789 
.0833 

Mean  17.721 

Mean  of  first  three    .0779 

Mean  of  all    .0793 

We  shall  see  immediately  that  the  temperature  of  the  bath 
makes  a  very  considerable  alteration  in  the  cooling  effect,  and 
we  therefore  select  the  first  three  results,  obtained  at  nearly  the 
same  temperature,  in  order  to  indicate  the  effect  of  pressure. 
On  referring  to  Chart  No.  3,  it  will  be  remarked  that  these 
three  results  range  themselves  almost  accurately  in  a  straight 
line.  Or,  by  looking  to  the  numbers  in  the  last  column,  we 
arrive  at  the  same  conclusion. 


FREE    EXPANSION    OF    GASES 


51 


MEMOIRS    ON    THE 

Cooling  Effect*  Experienced  by  Hydrogen  in  Passing  Through 

a  Porous  Plug. 

Not  having  been  able  as  yet  to  arrange  the  large  apparatus  so 
as  to  avoid  danger  in  using  this  gas  in  it,  we  have  contented 
ourselves  for  the  present  with  obtaining  a  determination  by  the 
help  of  the  smaller  force-pump  employed  in  our  preliminary 
experiments.  The  hydrogen,  after  passing  through  a  tube 
filled  with  fragments  of  caustic  potash,  was  forced,  at  a  press- 
ure of  68.4  Ibs.  on  the  inch,  through  a  piece  of  leather  in  con- 
tact with  the  bulb  of  a  small  thermometer,  the  latter  being 
protected  from  the  water  of  the  bath  by  a  piece  of  india-rubber 
tube.  At  a  temperature  of  about  10°  Cent,  a  slight  cooling 
effect  was  observed,  which  was  found  by  repeated  trials  to  be 
0°.076.  The  pressure  of  the  atmosphere  being  14.7  Ibs.,  it 
would  appear  that  the  cooling  effect  experienced  by  this  gas  is 
only  one-thirteenth  of  that  observed  with  atmospheric  air.  We 
state  this  result  with  some  reserve,  on  account  of  the  imperfec- 
tion of  such  experiments  on  a  small  scale,  but  there  can  be  no 
doubt  that  the  effect  of  hydrogen  is  vastly  inferior  to  that  of 
atmospheric  air. 

Influence  of  Temperature  on  the  Cooling  Effect. 
By  passing  steam  through  pipes  plunged  into  the  water  of 
the  bath  we  were  able  to  maintain  it  at  a  high  temperature 
without  a  considerable  variation.  The  passage  of  hot  air 
speedily  raised  the  temperature  of  the  stem  of  the  thermometer, 
as  well  as  of  the  glass  tube  in  which  it  was  enclosed ;  but  nev- 
ertheless the  precaution  was  taken  of  enclosing  the  whole  in  a 
tin  vessel,  by  means  of  which  water  in  constant  circulation 
with  the  water  of  the  bath  was  kept  within  one  or  two  inches 
of  the  level  of  the  mercury  in  the  thermometer.  The  bath  was 
completely  covered  with  a  wooden  lid,  and  the  water  kept  in 
constant  and  vigorous  agitation  by  a  proper  stirrer. 

[*  See  Part  IV.] 


FREE    EXPANSION     OF    GASES 


TABLE  XII. 

Experiment  in  which,  1st,  air;  3d,  carbonic  acid;  3d,  air,  dried  by  quick- 
lime, was  forced  through  a  plug  consisting  of  740  grs.  of  silk.     Mean 
barometric  pressure,  30.015,  equivalent  to  14.68  Ibs.  on  the  iuch. 
Gauge  under  the  atmospheric  pressure  150.     Percentage  of 
moisture  in  the  carb.onic  acid,  0.31.     Pump  placed  in  con- 
nection with  the  pipe  immersed  in  carbonic  acid  at 
llh-  24m\     Disconnected  and  attached  to  the 
quick-lime  cylinder  at  12h-  22m . 


Time  of 
Observa- 
tion 

Vol.  Percentage 
of  Carbonic  Acid 

Pressure  Gauge  and  Pressure 
in  Lbs.  on  the  Square  Inch 
Equivalent  Thereto 

Indication  of  Ther- 
mometer.    Tempera- 
ture of  the  Bath 

Indication  of  Ther- 
mometer.    Tempera- 
ture of  the  Issuing; 
Gas 

Cooling  Ef- 
fect in  Cent. 
Degrees 

H.        M. 

11       5 

0 

7 

0 

Ibs. 

9 

0 

31.62  =  91.508 

640.15  =  91°.  452 

478.  43  =  20°.  008 

1°.444 

11 

0 

13 

0 

15 

0 

17 

0 

19 

0 

21 

0 

31.95  =  90.570 

64(5.08  =  91°.442 

478.  58  =90°.  043 

i°.3£y 

22 

0 

23 

0 

24 

G 

25 

0 

26 

0 

30 

95.51  ) 

32 

95.51 

33 

95.51 

>95.51 

32.23=89.799 

646.  59  =  91°.  510 

409.63  =  S«°.  044 

3°.  472 

36 

95.51 

38 

95.51 

40 

43 

93.03  ' 

46 

48 

90.60 

>91.81 

32.1=90.162 

647.03=910.579 

470.57  =  88°.2o5 

3°.324 

50 

53 

80.82  '• 

55 

58 

12      0 

75.65 

,77.37 

32.16  =  90.006 

647.  5  =  91°.  647 

472.29  =  880.638 

3°.  009 

4 

6 

75.65 

9 

11 

65.72  : 

15 

60.83 

^62.46 

32.54  =  8C.971 

647.  94  =  91°.  711 

474.64  =  8i>°.162 

2°.  549 

20 

60.83 

22 

27 

0 

29 

0 

31 

0 

33 

0 

35 

0 

37 

0 

39 

0 

} 

41 

0 

1 

43 

0 

}.      32.3  =  89.618 

647.02=91°.578 

480.97=900.528 

10.050 

45 

0 

r 

47 

0 

49 

0 

j 

51 

0 

53 


UNIVERSITY 


MEMOIRS     ON     THE 


Although  hot  air  had  been  passed  through  the  plug  for  half 
an  hour  before  the  readings  in  the  preceding  table  were  ob- 
tained, it  is  probable  that  the  numbers  1.444  and  1.399,  repre- 
senting the  cooling  effect  of  atmospheric  air,  are  not  so  accurate 
as  the  value  1°.050.  Taking  this  latter  figure  for  the  effect  of 
an  excess  of  pressure  of  89.618-14.68  =  74.938  Ibs.,  we  find 
a  considerable  decrease  of  cooling  effect  owing  to  elevation 
of  temperature,  for  that  pressure,  at  the  low  temperatures 
previously  employed,  is  able  to  produce  a  cooling  effect  of 
1°.309. 

In  order  to  obtain  the  effect  of  carbonic  acid  unmixed  with 
atmospheric  air,  we  shall,  in  accordance  with  the  principle 
already  adhered  to,  consider  the  thermal  capacities  of  the  gases 
to  be  equal  for  equal  volumes.  Then  the  cooling  effect  of  the 
pure  gas 

_  3.472x100  —  1.052x4.49 

95.51 
Collecting  these  results  we  have  : 


=  3°.5S6. 


Temperature  of 
Bath 

Excess  of  Pressure 

Cooling  Effect 

Cooling  Kffect 
Reduced  to  100 
Lbs.  Pressure 

Theoretical  Cool- 
ing Effect  for 
100  Lbs.  Pressure 

12.844 
19.077 
91.516 

60.601 

87.248 
74.938 

5049 
2.938 
3.586 

8.33 
7.89 
4.78 

8.27 
8.07 
4.96 

NOTE. — The  numbers  shown  in  the  last  column  of  the  table  are  calculated  by 
the  general  expression  given  in  our  former  paper  (Phil.  7 Vans.,  July,  1853)  for 
the  cooling  effect,  from  an  empirical  formula  for  the  pressure  of  carbonic  acid, 
recently  communicated  by  Mr.  Rankine  in  a  letter  from  which  the  following  is 
extracted.  [Letter  omitted.] 

The  interpretation  given  above  for  the  experimental  results 
on  mixtures  of  carbonic  acid  and  air  depends  on  the  assump- 
tion (rendered  probable  as  a  very  close  approximation  to  the 
truth  by  Dalton's  law)  that  in  a  mixture  each  gas  retains  all 
its  physical  properties  unchanged  by  the  presence  of  the  other. 
This  assumption,  however,  may  be  only  approximately  true, 
perhaps  similar  in  accuracy  to  Boyle's  and  Gay-Lussac's  laws  of 
compression  and  expansion  by  heat ;  and  the  theory  of  gases 
would  be  very  much  advanced  by  accurate  comparative  experi- 
ments on  all  the  physical  properties  of  mixtures  and  of  their 

54 


FREE    EXPANSION     OF    GASES 

components  separately.  Towards  this  object  we  have  experi- 
mented on  the  thermal  effect  of  the  mutual  interpenetration  of 
carbonic  acid  and  air.  In  one  experiment  we  found  that  when 
7500  cubic  inches  of  carbonic  acid  at  the  atmospheric  pressure 
were  mixed  with  1000  cubic  inches  of  common  air,  and  a  per- 
fect mutual  interpenetration  had  taken  place,  the  temperature 
had  fallen  by  about  .2°  Cent.  We  intend  to  try  more  exact 
experiments  on  this  subject. 


THEOEETICAL  DEDUCTIONS 

SECTION  1. — On  the  Relation  letiveen  the  Heat  Evolved  and  the 

Work  Spent  in  Compressing  a  Gas  Kept  at 

Constant  Temperature. 

THIS  relation  is  not  a  relation  of  simple  mechanical  equiva- 
lence, as  was  supposed  by  Mayer*  in  his  Bemerlcungen  ueber  die 
Krafte  der  Unbelebten  Natur,  in  which  he  founded  on  it  an  at- 
tempt to  evaluate  numerically  the  mechanical  equivalent  of  the 
thermal  unit.  The  heat  evolved  may  be  less  than,  equal  to,  or 
greater  than  the  equivalent  of  the  work  spent,  according  as  the 
work  produces  other  effects  in  the  fluid  than  heat,  produces 
only  heat,  or  is  assisted  by  molecular  forces  in  generating  heat, 
and  according  to  the  quantity  of  heat,  greater  than,  equal  to, 
or  less  than  that  held  by  the  fluid  in  its  primitive  condition, 
which  it  must  hold  to  keep  itself  at  the  same  temperature  when 
compressed.  The  a  priori  assumption  of  equivalence,  for  the 
case  of  air,  without  some  special  reason  from  theory  or  experi- 
ment, is  not  less  unwarrantable  than  for  the  case  of  any  fluid 
whatever  subjected  to  compression.  Yet  it  may  be  demon- 
stratedf  that  water  below  its  temperature  of  maximum  density 
(39°.  1  Fahr.),  instead  of  evolving  any  heat  at  all  when  com- 
pressed, actually  absorbs  heat,  and  at  higher  temperatures 
evolves  heat  in  greater  or  less,  but  probably  always  very  small, 
proportion  to  the  equivalent  of  work  spent ;  while  air,  as  will 
be  shown  presently,  evolves  always,  at  least  when  kept  at  any 
temperature  between  0°  and  100°  Cent.,  somewhat  more  heat 


*  Annalen  of  WOhler  und  Liebig,  May,  1842. 

f  "  Dynamical  Theory  of  Heat,"  §  63,  equation  (b),  Trans.  Roy.  Soc. 
EcUnb.,  Vol.  XVI.,  p.  290  ;  or,  Phil.  Mag.,  Vol.  IV.,  Series  4,  p.  425. 

55 


MEMOIRS    ON    THE 

than  the  work  spent  in  compressing  it  could  alone  create. 
The  first  attempts  to  determine  the  relation  in  question,  for  the 
case  of  air,  established  an  approximate  equivalence  without 
deciding  how  close  it  might  be,  or  the  direction  of  the  discrep- 
ance, if  any.  Thus  experiments  "  On  the  Changes  of  Tempera- 
ture Produced  by  the  Rarefaction  and  Condensation  of  Air/'  * 
showed  an  approximate  agreement  between  the  heat  evolved  by 
compressing  air  into  a  strong  copper  vessel  under  water,  and 
the  heat  generated  by  an  equal  expenditure  of  work  in  stirring 
a  liquid  ;  and  again,  conversely,  an  approximate  compensation 
of  the  cold  of  expansion  when  air  in  expanding  spends  all  its 
work  in  stirring  its  own  mass  by  rushing  through  the  narrow 
passage  of  a  slightly  opened  stop-cock.  Again,  theory,  f  without 
any  doubtful  hypothesis,  showed  from  Regnault's  observations 
on  the  pressure  and  latent  heat  of  steam  that,  unless  the  density 
of  saturated  steam  differs  very  much  from  what  it  would  be  if 
following  the  gaseous  laws  of  expansion  and  compression,  the 
heat  evolved  by  the  compression  of  air  must  be  sensibly  less 
than  the  equivalent  of  the  work  spent  when  the  temperature  is 
as  low  as  0°  Cent.,  and  very  considerably  greater  than  the 
equivalent  when  the  temperature  is  above  40°  or  50°.  Mr. 
Rankine  is,  so  far  as  we  know,  the  only  other  writer  who  inde- 
pendently admitted  the  necessity  of  experiment  on  the  subject, 
and  he  was  probably  not  aware  of  the  experiments  that  had 
been  made  in  1844,  on  the  rarefaction  and  condensation  of  air, 
when  he  remarked^  that  "  the  value  of  K  is  unknown ;  and  as 
yet  no  experimental  data  exist  by  which  it  can  be  determined  " 
(K  denoting  in  his  expressions  a  quantity  the  vanishing  of 
which  for  any  gas  would  involve  the  equivalence  in  question). 
In  further  observing  that  K  is  probably  small  in  comparison 
with  the  reciprocal  of  the  coefficient  of  expansion,  Mr.  Rankine 
virtually  adopted  the  equivalence  as  probably  approximate  ; 
but  in  his  article  "  On  the  Thermic  Phenomena  of  Currents 

*  Communicated  to  the  Royal  Society,  June  20,  1844,  and  published  iu 
Philosophical  Magazine,  May,  1845. 

f  Appendix  to  "  Account  of  Carnot's  Theory,"  Roy.  Soc.  Edinb.,  April 
30,  1849,  Transactions.  Vol.  XVI.,  p.  568;  confirmed  in  the  "Dynamical 
Theory,"  §  22,  Trans.  Roy.  Soc.  Edinb.,  March  17, 1851 ;  and  Phil.  Mag.,  Vol. 
IV.,  Series  4,  p.  20. 

\  "Mechanical  Action  of  Heat,"  Section  II.  (10),  communicated  to  the 
Roy.  Soc.  Eilinb.,  Feb.  4,  1850;  Transactions,  Vol.  XX.,  p.  166. 

56 


FREE    EXPANSION     OF    GASES 

of  Elastic  Fluids/'*  he  took  the  first  opportunity  of  testing  it 
closely,  afforded  by  our  preliminary  experiments  on  the  thermal 
effects  of  air  escaping  through  narrow  passages. 

We  are  now  able  to  give  much  more  precise  answers  to  the 
question  regarding  the  heat  of  compression,  and  to  others 
which  rise  from  it,  than  those  preliminary  experiments  enabled 
us  to  do.  Thus  if  K  denote  the  specific  heat  under  constant 
pressure,  of  air  or  any  other  gas  issuing  from  the  plug  in  the 
experiments  described  above,  the  quantity  of  heat  that  would 
have  to  be  supplied,  per  pound  of  the  fluid  passing,  to  make 
the  issuing  stream  have  the  temperature  of  the  bath  would  be 
K£,  or 

(P-P') 

— — [n  is  the  atmospheric  pressure], 

where  m  is  equal  to  .26°  for  air  and  1°.15  for  carbonic  acid,  since 
we  found  that  the  cooling  effect  was  simply  proportional  to  the 
difference  of  pressure  in  each  case,  and  was  .0176°  per  pound 
per  square  inch,  or  .26°  per  atmosphere,  for  air,  and  about  4£ 
times  as  much  for  carbonic  acid.  This  shows  precisely  how 
much  the  heat  of  friction  in  the  plug  falls  short  of  compensat- 
ing the  cold  of  expansion.  But  the  heat  of  friction  is  the 
thermal  equivalent  of  all  the  work  done  actually  in  the  narrow 
passages  by  the  air  expanding  as  it  flows  through.  Now  this,  in 
the  cases  of  air  and  carbonic  acid,  is  really  not  as  much  as  the 
whole  work  of  expansion,  on  account  of  the  deviation  from 
Boyle's  law  to  which  these  gases  are  subject ;  but  it  exceeds 
the  whole  work  of  expansion  in  the  case  of  hydrogen,  which 
presents  a  contrary  deviation ;  since  P'V,  the  work  which  a 
pound  of  air  must  do  to  escape  against  the  atmospheric  press- 
ure, is,  for  the  two  former  gases,  rather  greater,  and  for  hydro- 
gen rather  less,  than  PV,  which  is  the  work  done  on  it  in  push- 
ing it  through  the  spiral  up  to  the  plug.  In  any  case,  w 
denoting  the  whole  work  of  expansion,  w— (P'V—  PV)  will 
be  the  work  actually  spent  in  friction  within  the  plug ;  and 


*  "  Mechanical  Action  of  Heat,"  Subsection  4,  communicated  to  the  Roy. 
Soc.  Edinb.,  Jan.  4,  1853;  Transactions,  Vol.  XX.,  p.  580. 

57 


MEMOIRS     ON    THE 

will  be  the  quantity  of  heat  into  which  it  is  converted,  a  quan- 
tity which,  in  the  cases  of  air  and  carbonic  acid,  falls  short  by 


of  compensating  the  cold  of  expansion.  If,  therefore,  H  de- 
note the  quantity  of  heat  that  would  exactly  compensate  the 
cold  of  expansion,  or  which  amounts  to  the  same,  the  quantity 
of  heat  that  would  be  evolved  by  compressing  a  pound  of  the 
gas  from  volume  V  to  the  volume  V,  when  kept  at  a  constant 
temperature,  we  have 


w  -  (P'V-  PV)  -  =  H  -  Km 


whence 

H  = 


Now  from  the  results  derived  by  Regnault  from  his  experiments 
on  the  compressibility  of  air,  of  carbonic  acid,  and  of  hydrogen, 
at  three  or  four  degrees  above  the  freezing-point,  we  find,  ap- 
proximately, 

P'V'-  PV         P-P7 

PV     ~  *     n~~ 

where  /=      .00082  for  air, 

/=      .0064  for  carbonic  acid, 
and  /—  -  .00043  for  hydrogen. 

No  doubt  the  deviations  from  Boyle's  law  will  be  somewhat 
different  at  the  higher  temperature  (about  15°  or  16°  Cent.)  of 
the  bath  in  our  experiments,  probably  a  little  smaller  for  air 
and  carbonic  acid,  and  possibly  greater  for  hydrogen  ;  but  the 
preceding  formula  may  express  them  accurately  enough  for  the 
rough  estimate  which  we  are  now  attempting. 
We  have,  therefore,  for  air  or  carbonic  acid  : 

P-P' 


w  -          w 


J      \  J    /      n          J 

58 


FREE    EXPANSION     OF    GASES 

The  values  of  JK  and  PV  for  the  three  gases  in  the  circum- 
stances of  the  experiments  are  as  follows  : 

For  atmospheric  air  JK  =  1390  x  .238  =  331  ; 
For  carbonic  acid  JK  =  1390  x  .217  =  301  ; 
For  hydrogen  JK  =  1390  x  3.4046  =  4732  ; 

and  for  atmospheric  air, 

at  15°  Cent.  PV  =  26224  (1  +  15  x  .00366)  =  27663  ; 
for  carbonic  acid, 

at  10°  Cent.  PV  =  17154  (1  +  10  x  .00366)  =  17782  ; 
for  hydrogen, 

at  10°  Cent.  PV  =  378960  (1  +  10  x  .00367)  =  393000. 

Hence  we  have,  for  air  and  carbonic  acid, 
w     PV     P-P' 


where  X  denotes  .0024  for  air,  and  .013  for  carbonic  acid,  show- 
ing (since  these  values  of  \  are  positive)  that  in  the  case  of 
each  of  these  gases  more  heat  is  evolved  in  compressing  it 
than  the  equivalent  of  the  work  spent  (a  conclusion  that  would 
hold  for  hydrogen  even  if  no  cooling  effect,  or  a  heating  effect 
less  than  a  certain  limit,  were  observed  for  it  in  our  form  of 
experiment).  To  find  the  proportion  which  this  excess  bears 
to  the  whole  heat  evolved,  or  to  the  thermal  equivalent  of  the 
work  spent  in  the  compression,  we  may  use  the  expression 


as  approximately  equal  to  the  mechanical  value  of  either  of 
those  energies  ;  and  we  thus  find  for  the  proportionate  excess  : 


p_p'  p_p' 

=  X  -     -    =  .0024  -     -    for  air, 


P—  P' 

or  =.013-    -^-  for  carbonic  acid. 


MEMOIRS     ON    THE 

This  equation  shows  in  what  proportion  the  heat  evolved  ex- 
ceeds the  equivalent  of  the  work  spent  in  any  particular  case 
of  compression  of  either  gas.  Thus  for  a  very  small  compres- 
sion from  P'  =  n,  the  atmospheric  pressure,  we  have 

p  /         p_  [j\       P—  IT 

lo£p  =  lo£  f  1  +  —  [j—  )  =  —  7f~  approximately, 

H-ito 

and  therefore  —  -  =  .0024  for  air 


or  =  .013    for  carbonic  acid. 

Therefore,  when  slightly  compressed  from  the  ordinary  atmos- 
pheric pressure,  and  kept  at  a  temperature  of  about  60°  Fahr., 
common  air  evolves  more  heat  by  ¥^-,  and  carbonic  acid  more 
by  Tf^-,  than  the  amount  mechanically  equivalent  to  the  work  of 
compression.  For  considerable  compressions  from  the  atmos- 
pheric pressure,  the  proportionate  excesses  of  the  heat  evolved 
are  greater  than  these  values,  in  the  ratio  of  the  Napierian 
logarithm  of  the  number  of  times  the  pressure  is  increased  to 
this  number  diminished  by  1.  Thus,  if  either  gas  be  com- 
pressed from  the  standard  state  to  double  density,  the  heat 
evolved  exceeds  the  thermal  equivalent  of  the  work  spent  by 
jg-J-o  in  the  case  of  air,  and  by  -fa  in  the  case  of  carbonic  acid. 

As  regards  these  two  gases,  it  appears  that  the  observed  cool- 
ing effect  was  chiefly  due  to  an  actual  preponderance  of  the 
mechanical  equivalent  of  the  heat  required  to  compensate  the 
cold  of  expansion  over  the  work  of  expansion,  but  that  rather 
more  than  one-fourth  of  it  in  the  case  of  air,  and  about  one-third 
of  it  in  the  case  of  carbonic  acid,  depended  on  a  portion  of  the 
work  of  expansion  going  to  do  the  extra  work  spent  by  the  gas 
in  issuing  against  the  atmospheric  pressure  above  that  gained 
by  it  in  being  sent  into  the  plug.  On  the  other  hand,  in  the 
case  of  hydrogen,  in  such  an  experiment  as  we  have  performed, 
there  would  be  a  heating  effect  if  the  work  of  expansion  were 
precisely  equal  to  the  mechanical  equivalent  of  the  cold  of 
expansion,  since  not  only  the  whole  work  of  expansion,  but  also 
the  excess  of  the  work  done  in  forcing  the  gas  in  above  that 

60 


FREE    EXPANSION     OF    GASES 

performed  by  it  in  escaping,  is  spent  in  friction  in  the  plug. 
Since  we  have  observed  actually  a  cooling  effect,  it  follows  that 
the  heat  absorbed  in  expansion  must  exceed  the  equivalent  of 
the  work  of  expansion,  enough  to  over-compensate  the  whole 
heat  of  friction  mechanically  equivalent,  as  this  is,  to  the  work 
of  expansion,  together  with  the  extra  work  of  sending  the  gas 
into  the  plug,  above  that  which  it  does  in  escaping.  In  the 
actual  experiment*  we  found  a  cooling  effect  of  .076°,  with  a 
difference  of  pressures,  P  —  P',  equal  to  53.7  Ibs.  per  square 
inch,  or  3.7  atmospheres.  Now  the  mechanical  value  of  the 
specific  heat  of  a  pound  of  hydrogen  is,  according  to  the  result 
stated  above,  4732  foot-pounds,  and  hence  the  mechanical  value 
of  the  heat  that  would  compensate  the  observed  cooling  effect 
per  pound  of  hydrogen  passing  is  360  foot-pounds.  But,  ac- 
cording to  Regnault's  experiments  on  the  compression  of  hy- 
drogen, quoted  above,  we  have 


PV-  P'V'=  PV  x  .00043      —    approximately  ; 

and  as  the  temperature  was  about  10°  in  our  experiment,  we 
have,  as  stated  above,  PV  =  393000. 

Hence,  for  the  case  of  the  experiment  in  which  the  difference 
of  pressure  was  3.7  atmospheres,  or 

P—  P' 


we  have  PV-P'V'  =  625; 

that  is,  625  f  oot-ponnds  more  of  work,  per  pound  of  hydrogen,  is 
spent  in  sending  the  hydrogen  into  the  plug  at  4.7  atmospheres 
of  pressures  than  would  be  gained  in  allowing  it  to  escape  at 
the  same  temperature  against  the  atmospheric  pressure.  Hence, 

*Frora  the  single  experiment  we  have  made  on  hydrogen  we  cannot 
conclude  that  at  other  pressures  a  cooling  effect  proportional  to  the  differ- 
ence of  pressures  would  be  observed,  and  therefore  we  confine  the  compar- 
ison of  the  three  gases  to  the  particular  pressure  used  in  the  hydrogen 
experiment.  It  should  be  remarked,  too,  that  we  feel  little  confidence  in 
the  value  assigned  to  the  thermal  effect  for  the  case  observed  in  the  experi- 
ment on  hydrogen,  and  only  consider  it  established  that  it  is  a  cooling 
effect,  and  very  small. 

61 


MEMOIRS     ON    THE 

the  heat  required  to  compensate  the  cold  of  expansion  is 
generated  by  friction  from  (1)  the  actual  work  of  expan- 
sion, together  with  (2)  the  extra  work  of  625  foot-pounds  per 
pound  of  gas,  and  (3)  the  amount  equivalent  to  360  foot-pounds 
which  would  have  to  be  communicated  from  without  to  do  away 
with  the  residual  cooling  effect  observed.  Its  mechanical 
equivalent,  therefore,  exceeds  the  work  of  expansion  by  985 
foot-pounds;  which  is  -^  of  its  own  amount,  since  the  work  of 
expansion  in  the  circumstances  is  approximately  393000  x 
log  4.7  =  608000  foot-pounds.  Conversely,  the  heat  evolved  by 
the  compression  of  hydrogen  at  10°  Cent.,  from  1  to  4.7  atmos- 
pheres, exceeds  by  ^-$  the  work  spent.  The  corresponding 
excess  in  the  case  of  atmospheric  air,  according  to  the  result 
obtained  above,  is  y^-¥,  and  in  the  case  of  carbonic  acid  -£%. 

It  is  important  to  observe  how  much  less  close  is  the  com- 
pensation in  carbonic  acid  than  in  either  of  the  other  gases, 
and  it  appears  probable  that  the  more  a  gas  deviates  from  the 
gaseous  laws,  or  the  more  it  approaches  the  condition  of  a  vapor 
at  saturation,  the  wider  will  be  the  discrepancy.  We  hope, 
with  a  view  to  investigating  further  the  physical  properties  of 
gases,  to  extend  our  method  of  experimenting  to  steam  (which 
will  probably  present  a  large  cooling  effect),  and  perhaps  to 
some  other  vapors. 

In  Mr.  Joule's  original  experiment*  to  test  the  relation  be- 
tween heat  evolved  and  work  spent  in  the  compression  of  air, 
without  an  independent  determination  of  the  mechanical  equiv- 
alent of  the  thermal  unit,  air  was  allowed  to  expand  through 
the  aperture  of  an  open  stopcock  from  one  copper  vessel  into 
another  previously  exhausted  by  an  air-pump  ;  and  the  whole 
external  thermal  effect  on  the  metal  of  the  vessels,  and  a  mass 
of  water  below  which  they  are  kept,  was  examined.  We  may 
now  estimate  the  actual  amount  of  that  external  thermal  effect, 
which  observation  only  showed  to  be  insensibly  small.  In  the 
first  place  it  is  to  be  remarked  that,  however  the  equilibrium 
of  pressure  and  temperature  is  established  between  the  two  air- 
vessels,  provided  only  no  appreciable  amount  of  work  is  emitted 
in  sound,  the  same  quantity  of  heat  must  be  absorbed  from  the 


*The  second  experiment  mentioned  in  the  abstract  published  in  the 
Proceedings  of  the  Royal  Society,  June  20,  1844,  and  described  in  the  Philo- 
sophical Magazine,  May,  1845,  p.  377.  [See  p.  17  of  this  volume.] 

62 


FREE     EXPANSION     OF    GASES 

copper  and  water  to  reduce  them  to  their  primitive  tempera- 
ture ;  and  that  this  quantity,  as  was  shown  above,  is  equal  to 

PV  P-P'      27000x0.0024      P-F  aP~P' 

X  0.0024  x =  -  -  x  — -  — -  =  0.046 


j  ii  1390  n  n 

In  the  actual  experiments  the  exhausted  vessel  was  equal  in 
capacity  to  the  charged  vessel,  and  the  latter  contained.  13  of 
a  pound  of  air,  under  21  atmospheres  of  pressure,  at  the  com- 
mencement. Hence,  P'=  JP  and 

P-P' 

=  10.5  ; 


n 

and  the  quantity  of  heat  required  from  without  to  compensate 
the  total  internal  cooling  effect  must  have  been 

. 046  x  10.5  x. 13  =  .063. 

This  amount  of  heat  taken  from  16^  Ibs.  of  water,  28  Ibs.  of 
copper,  and  7  Ibs.  of  tinned  iron,  as  in  the  actual  experiment, 
would  produce  a  lowering  of  temperature  of  only  .003°  Cent. 
We  need  not  therefore  wonder  that  no  sensible  external  ther- 
mal effect  was  the  result  of  the  experiment  when  the  two 
copper  vessels  and  the  pipe  connecting  them  were  kept  under 
water,  stirred  about  through  the  whole  space  surrounding 
them,  and  that  similar  experiments,  more  recently  made  by  M. 
Regnault,  should  have  led  only  to  the  same  negative  conclusion. 
If,  on  the  other  hand,  the  air  were  neither  allowed  to  take  in 
heat  from  nor  to  part  with  heat  to  the  surrounding  matter  in 
any  part  of  the  apparatus,  it  would  experience  a  resultant  cool- 
ing effect  (after  arriving  at  a  state  of  uniformity  of  temperature 
as  well  as  pressure)  to  be  calculated  by  dividing  the  preceding 
expression  for  the  quantity  of  heat  which  would  be  required  to 
compensate  it  by  .17,  the  specific  heat  of  air  under  constant 
pressure.  The  cooling  effect  on  the  air  itself,  therefore, 
amounts  to 

p_F  * 


0°.27  x 


n 


*  It  is  worthy  of  remark  that  this,  the  expression  for  the  cooling  effect 
experienced  by  a  mass  of  atmospheric  air  expanding  from  a  bulk  in  which 

63 


MEMOIRS     ON     THE 

which  is  equal  to  2°. 8,  for  air  expanding,  as  in  Mr.  Joule's 
experiment,  from  21  atmospheres  to  half  that  pressure,  and  is 
900  times  as  great  as  the  thermometric  effect  when  spread  over 
the  water  and  copper  of  the  apparatus.  Hence  our  present 
system,  in  which  the  thermometric  effect  on  the  air  itself  is 
directly  observed,  affords  a  test  hundreds  of  times  more  sensi- 
tive than  the  method  first  adopted  by  Mr.  Joule,  and  no  doubt 
also  than  that  recently  practised  by  M.  Regnault,  in  which  the 
dimensions  of  the  various  parts  of  the  apparatus  (although  not 
yet  published)  must  have  been  on  a  corresponding  scale,  or  in 
somewhat  similar  proportions,  to  those  used  formerly  by  Mr. 
Joule. 


SECTION   II. — On  the  Density  of  Saturated  Steam. 

The  relation  between  the  heat  evolved  and  the  work  spent, 
approximately  established  by  the  air  experiments  communi- 
cated to  the  Royal  Society  in  1844,  was  subjected  to  an  inde- 
pendent indirect  test  by  an  application  of  Carnot's  theory, 
with  values  of  "  Carnot's  function,"  which  had  been  calculated 
from  Regnault's  data  as  to  the  pressure  and  latent  heat  of 
steam,  and  the  assumption  (in  want  of  experimental  data)  that 
the  density  varies  according  to  the  gaseous  laws.  The  verifica- 
tion thus  obtained  was  very  striking,  showing  an  exact  agree- 
ment with  the  relation  of  equivalence  at  a  temperature  a  little 
above  that  of  observation,  and  an  agreement  with  the  actual 
experimental  results  quite  within  the  limits  of  the  errors  of 
observation ;  but  a  very  wide  discrepancy  from  equivalence  for 
other  temperatures.  The  following  table  is  extracted  from  the 
appendix  to  the  "Account  of  Carnot's  Theory,"  in  which  the 
theoretical  comparison  was  first  made,  to  facilitate  a  compari- 
son with  what  we  now  know  to  be  the  true  circumstances  of  the 
case. 


its  pressure  is  P  to  a  bulk  in  which,  at  the  same  (or  very  nearly  the  same) 
temperature,  its  pressure  is  P',  and  spending  all  its  work  of  expansion  in 
friction  among  its  own  particles,  agrees  very  closely  with  the  expression 

P  — P 

.26  x for  the  cooling  effect  in  the  somewhat  different  circumstances 

of  our  experiments. 

64 


FREE    EXPANSION     OF     GASES 
"  Table  of  the  Values  of 


"Work  requisite  to  pro- 
duce a  unit  of  heat  by 
the  compression  of  a 

"Temperature    of  the 

gas 

•'Work  requisite  to  pro- 
duce a  unit  of  heat  by 
the  compression  of  a 

"Temperature    of  the 

gas 

gas 

J 

gas 

f 

E          ~[     ' 

ft.  Ibs. 

0 

ft.  Ibs. 

0 

1357.1 

0 

14464 

120 

13687 

10 

1455.8 

130 

1379.0 

20 

1465.3 

140 

1388.0 

30 

1475.8 

150 

1395.7 

40 

1489.2 

160 

1401.8 

50 

1499.0 

170 

1406.7 

60 

1511.3 

180 

1412.0 

70 

1523.5 

190 

1417.6 

80 

1536.5 

200 

1424.0 

90 

1550.2 

210 

1430.6 

100 

1564.0 

220 

1438.2 

110 

1577.8 

230" 

We  know  from  the  experiments  described  above  in  the  present 
paper  that  the  numbers  in  the  first  column,  and,  we  may  con- 
clude with  almost  equal  certainty,  that  the  numbers  in  the 
third  also,  ought  to  be  each  very  nearly  the  mechanical  equiv- 
alent of  the  thermal  unit.  This  having  been  ascertained  to  be 
1390  (for  the  thermal  unit  Centigrade)  by  the  experiments  on 
the  friction  of  fluids  and  solids,  communicated  to  the  Royal 
Society  in  1849,  and  the  work  having  been  found  above  to  fall 
short  of  the  equivalent  of  the  heat  produced  by  about  3-^,  at 
the  temperature  of  the  air  experiments  at  present  communi- 
cated, and  by  somewhat  less  at  such  a  higher  temperature  as 
30°,  we  may  infer  that  the  agreement  of  the  tabulated  theoreti- 
cal result  with  the  fact  is  perfect  at  about  30°  Cent.  Or,  neg- 
lecting the  small  discrepance  by  which  the  work  truly  required 
falls  short  of  the  equivalent  of  the  heat  produced,  we  may  con- 
clude that  the  true  value  of  ^-S — -  for  all  temperatures  is 

Jjj 

about  1390 ;  and  hence  that  if  [W]  denote  the  numbers  shown 
for  it  in  the  preceding  table,  /u  the  true  value  of  Carnot's  func- 
tion, and  [p~\  the  value  tabulated  for  any  temperature  in  the 
"Account  of  Carnot's  Theory,"  we  must  have  to  a  very  close 
degree  of  approximation, 

E  65 


MEMOIRS    ON    THE 

-r       139° 
X[WT 

But  if  [v]  denote  the  formerly  assumed  specific  gravity  of  sat- 
urated steam,  p  its  pressure,  and  X  its  latent  heat  per  pound  of 
matter,  and  if  p  be  the  mass  (in  pounds)  of  water  in  a  cubic 
foot,  the  expression  from  which  the  tabulated  values  of  [/*] 
were  calculated  is 

p[ff]    *di  ' 

while  the  true  expression  of  Carnot's  function  in  terms  of 
properties  of  steam  is 

_1-(T  Idp 
ptr     X  dt 
Hence, 


[/•]  "  '   i-M' 

or,  approximately,  since  o-  and  [<r]  are  small  fractions, 


M 

We  have,  therefore, 


[<r]  -  1390  ' 

and  we  infer  that  the  densities  of  saturated  steam  in  reality 
bear  the  same  proportions  to  the  densities  assumed,  according 
to  the  gaseous  laws,  as  the  numbers  shown  for  different  tem- 
peratures in  the  preceding  table  bear  to  1390.  Thus  we  see 
that  the  assumed  density  must  have  been  very  nearly  correct, 
about  30?  Cent.,  but  that  the  true  density  increases  much  more 
at  the  high  temperatures  and  pressures  than  according  to  the 
gaseous  laws,  and  consequently  that  steam  appears  to  deviate 
from  Boyle's  law  in  the  same  direction  as  carbonic  acid,  but  to 
a  much  greater  amount,  which,  in  fact,  it  must  do  unless  its 
coefficient  of  expansion  is  very  much  less,  instead  of  being,  as 
it  probably  is,  somewhat  greater  than  for  air.  Also,  we  infer 
that  the  specific  gravity  of  steam  at  100°  Cent.,  instead  of  be- 

66 


FREE    EXPANSION    OF    GASES 


iug  only  y^-g-.-g-,  as  was  assumed,  or  about  -p^,  as  it  is  generally 
supposed  to  be,  must  be  as  great  as  y-gVs--  Without  using  the 
preceding  table,  we  may  determine  the  absolute  density  of 
saturated  steam  by  means  of  a  formula  obtained  as  follows. 
Since  we  have  seen  the  true  value  of  W  is  nearly  1390,  we  must 
have,  very  approximately, 

1390  E 


and  hence,  according  to  the  preceding  expression  for  /*  in  terms 
of  the  properties  of  steam, 


or,  within  the  degree  of  approximation  to  which  we  are  going 
(omitting  as  we  do  fractions  such  as  j^  of  the  quantity  evalu- 
ated), 

l  +  Et  dp 
"1390  EX  dt' 

an  equation  by  which  py,  the  mass  of  a  cubic  foot  of  steam,  in 
fractions  of  a  pound,  or  r,  its  specific  gravity  (the  value  of  p 
being  63.887),  may  be  calculated  from  observations  such  as 
those  of  Eegnault  on  steam.  Thus,  using  Mr.  Kankine's  em- 
pirical formula  for  the  pressure  which  represents  M.  Regnault's 
own  formula  for  the  latent  heat,  and  taking  E  =  -^9  we  have 


_ 


1390       (606.5  +  0.305  /)-(*  +  .  00002  *"  +  .  0000003  t3)' 


with  the  following  equations  for  calculating  p  and  the  terms 
involving  /3  and  y  : 

n 


t  +  274.6       (£  + 274.6)" 
a  =  4.950433  +  Iog10  2114  =  8.275538, 
log10/3  =  3.1851091, 
togioy  =  5.0827176. 
67 


MEMOIRS    ON    THE 

The  densities  of  saturated  steam  calculated  for  any  tempera- 
tures, either  by  means  of  this  formula,  or  by  the  expression 
given  above,  with  the  assistance  of  the  table  of  values  of  [W], 
are  the  same  as  those  which,  in  corresponding  on  the  subject 
in  1848,  we  found  would  be  required  to  reconcile  Eegnault's 
actual  observations  on  steam  with  the  results  of  air  experiments 
which  we  then  contemplated  undertaking,  should  they  turn 
out,  as  we  now  find  they  do,  to  confirm  the  relations  which  the 
air  experiments  of  1844  had  approximately  established.  They 
should  agree  with  results  which  Clausius*  gave  as  a  conse- 
quence of  his  extension  of  Carnot's  principle  to  the  dynamical 
theory  of  heat,  and  his  assumption  of  Mayer's  hypothesis. 


SECTION  III.  —  Evaluation  of  Carnot's  Function. 

The  importance  of  this  object,  not  only  for  calculating  the 
efficiency  of  steam-engines  and  air-engines,  but  for  advancing 
the  theory  of  heat  and  thermo-electricity,  was  a  principal  rea- 
son for  inducing  us  to  undertake  the  present  investigation. 
Our  preliminary  experiments,  demonstrating  that  the  cooling 
effect  which  we  discovered  in  all  of  them  was  very  slight  for  a 
considerable  variety  of  temperatures  (from  about  0°  to  77°  Cent.  ), 
were  sufficient  to  show,  as  we  have  seen  in  §§  I.  and  II.,  that 

—  —  ^  -  *  must  be  very  nearly  equal  to  the  mechanical  equiva- 
lent of  the  thermal  unit  ;  and  therefore  we  have 

fi  =  -^  -  approximately, 


or,  taking  for  E  the  standard  coefficient  of  expansion  of  atmos- 
pheric air,  .003665, 

J 
P      272.85  +  /' 

At  the  commencement  of  our  first  communication  to  the  Royal 

*Poggendorff's  Annalen,  April  and  May,  1850. 
68 


FREE    EXPANSION    OF    GASES 

Society  on  the  subject  we  proposed  to  deduce  more  precise 
values  for  this  function  by  means  of  the  equation 

JKa-(P'V'-PV)  +  w. 


dw 


where  V' 

w  =   I  pdv  ; 
V 

v,  V,  V  denote,  with  reference  to  air  at  the  temperature  of  the 
bath,  respectively,  the  volumes  occupied  by  a  pound  under  any 
pressure  p,  under  a  pressure  P,  equal  to  that  with  which  the 
air  enters  the  plug,  and  under  a  pressure  P',  with  which  the 
air  escapes  from  the  plug  ;  and  JK3  is  the  mechanical  equiva- 
lent of  the  amount  of  heat  per  pound  of  air  passing  that  would 
be  required  to  compensate  the  observed  cooling  effect  3.  The 

direct  use  of  this  equation  for  determining  —  requires,  besides 

P- 
our  own  results,  information  as  to  compressibility  or  expan- 

sion, which  is  as  yet  but  very  insufficiently  afforded  by  direct 
experiments,  and  is  consequently  very  unsatisfactory,  so  much 
so  that  we  shall  only  give  an  outline,  without  details,  of  two 
plans  we  have  followed,  and  mention  the  results.  First,  it  may 
be  remarked  that,  approximately, 

P  fltn  P 

w  =  (1  +  EO  H  log  p,  and  ^  =  EH  log  p, 

H  being  the  "  height  of  the  homogeneous  atmosphere,"  or  the 
product  of  the  pressure  into  the  volume  of  a  pound  of  air,  at 
0°  Cent.  ;  of  which  the  value  is  26224  feet.  Hence  if  E  denote 
a  certain  mean  coefficient  of  expansion  suitable  to  the  circum- 
stances of  each  individual  experiment,  it  is  easily  seen  that 

•j—  may  be  put  under  the  form  -—  -  -f  t  \ 

~dt 

and  thus  we  have 

69 


MEMOIRS    ON    THE 
J        1  JKS-(P'V'-PV) 

-  =   -=     +    '+-  —  p  -  ) 

EH  log  ^ 

since  the  numerator  of  the  fraction  constituting  the  last  term 
is  so  small  that  the  approximate  value  may  be  used  for  the  de- 
nominator. The  first  term  of  the  second  member  may  easily 
be  determined  analytically  in  general  terms  ;  but  as  it  has  ref- 
erence to  the  rate  of  expansion  at  the  particular  temperature 
of  the  experiment,  and  not  to  the  mean  expansion  from  0°  to 
100°,  which  alone  hae  been  investigated  by  Regnault  and  oth- 
ers who  have  made  sufficiently  accurate  experiments,  we  have 
not  data  for  determining  its  values  for  the  particular  cases  of 
the  experiments.  We  may,  however,  failing  more  precise  data, 
consider  the  expansion  of  air  as  uniform  from  0°  to  100°  for 
any  pressure  within  the  limits  of  the  experiments  (four  or  five 
atmospheres),  because  it  is  so  for  air  at  the  atmospheric  density 
by  the  hypothesis  of  the  air-thermometer;  and  Kegnault's  com- 
parisons of  air-thermometers  in  different  conditions  show  for 
all,  whether  on  the  constant-volume  or  constant-pressure  prin- 
ciple, with  density  or  pressure  from  one  -  half  to  double  the 
standard  density  or  pressure,  a  very  close  agreement  with  the 
standard  air-thermometer.  On  this  assumption,  then,  when  we 
take  into  account  Regnault's  observations  regarding  the  effect 
of  the  variations  of  density  on  the  coefficient  of  increase  of 
pressure,  we  find  that  a  suitable  mean  coefficient  E  for  the 

circumstances  of  the  preceding  formula  for  —  is  expressed  to 

P- 
a  sufficient  degree  of  approximation  by  the  equation 

-0000441   P- 


=  .  0036534 


3.81 


Also  by  using  Regnault's  experimental  results  on  compressibil- 
ity of  air  as  if  they  had  been  made,  not  at  4°.  75,  but  at  16° 
Cent.,  we  have  estimated  P'V — PV  for  the  numerator  of  the 
last  term  of  the  preceding  expression.  We  have  thus  obtained 

estimates  for  the  value  of  —  from  eight  of  our  experiments  (not 

corresponding  exactly  to  the  arrangement  in  seven  series  given 

70 


FREE     EXPANSION     OF     GASES 


above),  which,  with  the  various  items  of  the  correction  in  the 
case  of  each  experiment,  are  shown  in  the  following  table  : 


Correction 

Value  of  J 

N'o.  of 
Exp. 

of  Air 
Forced 
into  the 

Baro- 
metric 
Press- 
ure 

Excess 

Cooling 
Effect 

Correction 
by  Cooling 
Effect 

by  Recip- 
rocal Co- 
efficient of 
Expan- 

Correction 
by  Compres- 
sibility (Sub- 
tracted) 

divided  by 
Carnot's 
Function 
for  16° 

sion 

Cent. 

JK6 

1         1 

p'V—  PV 

j 

P 

P' 

P  —  P' 

a 

p 

p 

EH  log  -p 

E       E 

EH  log  — 

Ml6 

0 

J, 

20.94314.777 

6.166 

0.105 

1.031 

0.174 

0.290 

289.4 

11.21.28214.326 

6.956 

0.109 

0.942 

0.168 

0.291 

289.3 

III.  35.  822  14.  504 

21.318 

0.375 

1.421 

0.519 

0.412 

289.97 

IV.  33.31014.692   18.618 

0.364 

1.523 

0.470 

0.372 

290.065 

V. 

55.44114.610 

40.831 

0.740 

1.892 

0.923 

0.480 

289.705 

VI. 

53.  471  !  14.  571 

38.900 

0.676 

1.814 

0.883 

0.475 

289.59 

VII. 

79.464 

14.955 

64.509 

1.116 

2.272 

1.379 

0.592 

289.69 

VIII. 

79.967 

14.785 

65.182 

1.142 

2.300 

1.376 

0.586 

289.73 

Mean  .  .  . 

289.68 

In  consequence  of  the  approximate  equality  of  —  to  -^r  +  t, 

n        -bj 

its  value  must  be,  within  a  very  minute  fraction,  less  by  16  at 
0°  than  at  16°  ;  and  from  the  mean  result  of  the  table  we 

therefore  deduce  273.68  as  the  value  of  —  at  the  freezing- 

P 

point.  The  correction  thus  obtained  on  the  approximate  esti- 
mate -=r+t  =  272.85  +  t,  for  — ,  at  temperatures  not  much 
above  the  freezing-point,  is  an  augmentation  of  .83. 

For  calculating  the  unknown  terms  in  the  expression  for  — 

H- 
we  have  also  used  Mr.  Rankine's  formula  for  the  pressure  of 

air,  which  is  as  follows  : 


where 


C  =  274.6,  Iog10<*  =  .3176168,  Iog107*  =  3.8181546, 
26224 


II 


1  -  a  +  h9 
71 


MEMOIRS     ON     THE 

and,  v  being  the  volume  of  a  pound  of  air  when  at  the  tempera- 
ture t  and  under  the  pressure^,  p  denotes  the  mass  in  pounds 
of  a  cubic  foot  at  the  standard  atmospheric  pressure  of  29.9218 
inches  of  mercury.  The  value  of  p  according  to  this  equation, 

when  substituted  in  the  general  expression  for  -L  gives  : 


JKCA,q,      Cl 

-ird  +  m(c^rt 


From  this  we  find,  with  the  data  of  the  eight  experiments  just 
quoted,  the  following  values  of  —  at  the  temperature  of  16°  Cent. , 

289.044,  289.008,  288.849,  289.112,  288.787,  288.722,  288.505, 

288.559,  the  mean  of  which  is  288.82, 

giving  a  correction  of  only  .03  to  be  subtracted  from  the  pre- 
vious approximate  estimate  -~-  -\-t. 

It  should  be  observed  that  Carnot's  function  varies  only  with 
the  temperature  ;  and,  therefore,  if  such  an  expression  as  the 
preceding,  derived  from  Mr.  Rankine's  formula,  be  correct,  the 
cooling  effect,  £,  must  vary  with  the  pressure  and  temperature 
in  such  a  way  as  to  reduce  the  complex  fraction,  constituting 
the  second  term,  to  either  a  constant  or  a  function  of  t.  Now 
at  the  temperature  of  our  experiments,  3  is  very  approximately 
proportional  to  simply  P— P',  and  therefore  all  the  terms  in- 
volving the  pressure  in  the  numerator  ought  to  be  either  linear 
or  logarithmic  ;  and  the  linear  terms  should  balance  one  another 

p 
so  as  to  leave  only  terms  which,  when  divided  by  log  -=57,  become 

independent  of  the  pressures.  This  condition  is  not  fulfilled 
by  the  actual  expression,  but  the  calculated  results  agree  with 
one  another  as  closely  as  could  be  expected  from  a  formula  ob- 
tained with  such  insufficient  experimental  data  as  Mr.  Rankine 
had  for  investigating  the  empirical  forms  which  his  theory  left 
undetermined.  We  shall  see  in  Section  V.  below  that  simpler 
forms  represent  Regnault's  data  within  their  limits  of  error  of 

72 


FREE     EXPANSION    OF    GASES 

observation,  and  at  the  same  time  may  be  reduced  to  consist- 
ency in  the  present  application. 

As  yet  we  have  no  data  regarding  the  cooling  effect  of  suf- 
ficient accuracy  for  attempting  an  independent  evaluation  of 
Carnot's  function  for  other  temperatures.  In  the  following 
section,  however,  we  propose  a  new  system  of  thermometry, 
the  adoption  of  which  will  quite  alter  the  form  in  which  such 
a  problem  as  that  of  evaluating  Carnot' s  function  for  any  tem- 
perature presents  itself. 


SECTION"  IV. — On  an  Absolute  Tliermometric  Scale  Founded 
on  the  Mechanical  Action  of  Heat. 

In  a  communication  to  the  Cambridge  Philosophical  Society  * 
six  years  ago  it  was  pointed  out  that  any  system  of  thermometry 
founded  either  on  equal  additions  of  heat,  or  equal  expansions, 
or  equal  augmentations  of  pressure,  must  depend  on  the  par- 
ticular thermometric  substance  chosen,  since  the  specific  heats, 
the  expansions,  and  the  elasticities  of  substances  vary,  and,  so 
far  as  we  know,  not  proportionally  with  absolute  rigour  for  any 
two  substances.  Even  the  air-thermometer  does  not  afford  a, 
perfect  standard  unless  the  precise  constitution  and  physical 
state  of  the  gas  used  (the  density,  for  a  pressure-thermometer, 
or  the  pressure,  for  an  expansion-thermometer)  be  prescribed  ; 
but  the  very  close  agreement  which  Regnault  found  between 
different  air-  and  gas-thermometers  removes,  for  all  practical 
purposes,  the  inconvenient  narrowness  of  the  restriction  to  at- 
mospheric air  kept  permanently  at  its  standard  density,  imposed 
on  the  thermometric  substance  in  laying  down  a  rigorous  defi- 
nition of  temperature.  It  appears,  then,  that  the  standard  of 
practical  thermometry  consists  essentially  in  the  reference  to 
a  certain  numerically  expressible  quality  of  a  particular  sub- 
stance. In  the  communication  alluded  to,  the  question,  "  Is 
there  any  principle  on  which  an  absolute  thermometric  scale 
can  be  founded  ?"  was  answered  by  showing  that  Carnot's  func- 

*  "  On  an  Absolute  Thermometric  Scale  Founded  on  Carnot's  Theory  of 
the  Motive  Power  of  Heat,  and  Calculated  from  Regnault's  Observations 
on  Steam,"  by  Professor  W.  Thomson  ^Proceedings  Camb.  Phil.  8oc.,  June 
5,  1848,  or  Philosophical  Magazine,  October,  1848. 

73 


MEMOIRS    ON    THE 

tion  (derivable  from  the  properties  of  any  substance  whatever, 
but  the  same  for  all  bodies  at  the  same  temperature),  or  any 
arbitrary  function  of  Carnot's  function,  may  be  defined  as  tem- 
perature, and  'is  therefore  the  foundation  of  an  absolute  sys- 
tem of  thermometry.  We  may  now  adopt  this  suggestion  with 
great  advantage,  since  we  have  found  that  Garnet's  function 
varies  very  nearly  in  the  inverse  ratio  of  what  has  been  called 
" temperature  from  the  zero  of  the  air-thermometer" — that  is, 
Centigrade  temperature  by  the  air-thermometer  increased  by 
the  reciprocal  of  the  coefficient  of  expansion ;  and  we  may  de- 
fine temperature  simply  as  the  reciprocal  of  Garnet's  function. 
When  we  take  into  account  what  has  been  proved  regarding 
the  mechanical  action  of  heat,*  and  consider  what  is  meant  by 
Garnet's  function,  we  see  that  the  following  explicit  definition 
may  be  substituted  : 

If  any  substance  whatever,  subjected  to  a  perfectly  reversible 
cycle  of  operations,  takes  in  heat  only  in  a  locality  kept  at  a  uni- 
form temperature,  and  emits  heat  only  in  another  locality  kept 
at  a  uniform  temperature,  the  temperatures  of  these  localities  are 
proportional  to  the  quantities  of  heat  taken  in  or  emitted  at  them 
in  a  complete  cycle  of  the  operations. 

To  fix  on  a  unit  or  degree  for  the  numerical  measurement  of 
temperature,  we  may  either  call  some  definite  temperature,  such 
as  that  of  melting  ice,  unity,  or  any  number  we  please  ;  or  we 
may  choose  two  definite  temperatures,  such  as  that  of  melting 
ice  and  that  of  saturated  vapour  of  water  under  the  pressure 
29.9218  inches  of  mercury  in  the  latitude  45°,  and  call  the  dif- 
ference of  these  temperatures  any  number  we  please — 100,  for 
instance.  The  latter  assumption  is  the  only  one  that  can  be 
made  conveniently  in  the  present  state  of  science,  on  account 
of  the  necessity  of  retaining  a  connection  with  practical  ther- 
mometry as  hitherto  practised  ;  but  the  former  is  far  prefer- 
able in  the  abstract,  and  must  be  adopted  ultimately.  In  the 
meantime  it  becomes  a  question,  What  is  the  temperature  of 
melting  ice,  if  the  difference  between  it  and  the  standard  boil- 
ing-point be  called  100°  ?  When  the  question  is  answered  with- 
in a  tenth  of  a  degree  or  so,  it  may  be  convenient  to  alter  the 

*  Dynamical  Theory  of  Heat,  §§  42,  43. 
74 


FREE    EXPANSION    OF    GASES 

foundation  on  which  the  degree  is  defined  by  assuming  the 
temperature  of  melting  ice  to  agree  with  that  which  has  been 
found  in  terms  of  the  old  degree ;  and  then  to  make  it  an  ob- 
ject of  further  experimental  research,  to  determine  by  what 
minute  fraction  the  range  from  freezing  to  the  present  stand- 
ard boiling  point  exceeds  or  falls  short  of  100.  The  experi- 
mental data  at  present  available  do  not  enable  us  to  assign  the 
temperature  of  melting  ice,  according  to  the  new  scale,  to  per- 
fect certainty  within  less  than  two  or  three  tenths  of  a  degree ; 
but  we  shall  see  that  its  value  is  probably  273.7,  agreeing  with 

the  value  —  at  0°  found  by  the  first  method  in  Section  III. 
t* 

From  the  very  close  approximation  to  equality  between  --  and 

^  +  t,  which  our  experiments  have  established,  we  may  be 

sure  that  the  temperature  from  the  freezing-point  by  the  new 
system  must  agree  to  a  very  minute  fraction  of  a  degree  with 
Centigrade  temperature  between  the  two  prescribed  points  of 
agreement,  0°  and  100°,  and  we  may  consider  it  as  highly  prob- 
able that  there  will  also  be  a  very  close  agreement  through 
a  wide  range  on  each  side  of  these  limits.  It  becomes,  of 
course,  an  object  of  the  greatest  importance,  when  the  new  sys- 
tem is  adopted,  to  compare  it  with  the  old  standard  ;  and  this 
is,  in  fact,  what  is  substituted  for  the  problem,  the  evaluation 
of  Carnot's  function,  now  that  it  is  proposed  to  call  the  recip- 
rocal of  Carnot's  function,  temperature.  In  the  next  section 
we  shall  see  by  what  kind  of  an  examination  of  the  physical 
properties  of  air  this  is  to  be  done,  and  investigate  an  empiri- 
cal formula  expressing  them  consistently  with  all  the  experi- 
mental data  as  yet  to  be  had,  so  far  as  we  know. 

The  following  table,  showing  the  indications  of  the  con- 
stant-volume and  constant -pressure  air -thermometer  in  com- 
parison for  every  twenty  degrees  of  the  new  scale,  from  the 
freezing-point  to  300°  above  it,  has  been  calculated  from  the 
formulae  (9),  (10),  and  (39)  of  Section  V.  below. 


MEMOIRS     ON    THE 


COMPARISON    OF    AIR-THERMOMETER  WITH    ABSOLUTE    SCALE 


Temperature  by  Absolute 
Scale  in  Cent.  Degrees 
from  the  Freezing- 
point 

Temperature  Centigrade  by  Con. 
stant-volume  Thermometer 
with  Air  of  Specific 

Gravity  — 

V 

Temperature  Centigrade  by  Con- 
stant-pressure Air- 
thermometer 

t  —  273.7 

/i  inn                  **o.7 

-      loo    Vt~v™-'1 

"  :=  J.UU 
^373.7  —  ^473.7 

o 

0 

O 

0 

o 

0 

20 

20  +.0298  x  — 

20+.  0404  x  j- 

V 

u 

40 

40  +.0403 

40  +.0477 

60 

60  +.0366 

60  +.0467 

80 

80  +.0223 

80  +.0277 

100 

100  +.0000 

100  +.0000 

120 

120  -.0284 

120  -.0339 

140 

140  -.0615 

140  -.0721 

160 

160  -.0983 

160  -.1134 

180 

180  -.1382 

180  -.1571 

200 

200  -.1796 

200  -.2018 

220 

220  -.2232 

220  -.2478 

240 

240  -.2663 

240  -.2932 

260 

260  -.3141 

260  -.3420 

280 

280  -.3610 

280  -.3897 

300 

300  -.4085 

300  -.4377 

The  standard  defined  by  Regnault  is  that  of  the  constant-vol- 
ume air-thermometer,  with  air  at  the  density  which  it  has  when  at 
the  freezing-point  under  the  pressure  of  760  mm.,  or  29.9218 
inches  of  mercury,  and  its  indications  are  shown  in  comparison 


with  the  absolute  scale  by  taking  —  = 


in  the  second  column  of 


the  preceding  table.  The  greatest  discrepance  between  0°  and 
100°  Cent,  amounts  to  less  than  •£$  of  a  degree,  and  the  discrep- 
ance at  300°  Cent,  is  only  four-tenths.  The  discrepancies  of 
the  constant  -  pressure  air-  thermometer,  when  the  pressure  is 

fY\ 

equal  to  the  standard  atmospheric  pressure,  or  —  =  1,  are 
somewhat  greater,  but  still  very  small. 


SECTION  V.  —  Physical  Properties  of  Air  Expressed  according 
to  the  Absolute  Thermodynamic  Scale  of  Temperature. 

All  the  physical  properties  of  a  fluid  of  given  constitution 
are  completely  fixed  when  its  density  and  temperature  are  speci- 

76 


FREE     EXPANSION     OF     GASES 

fied  ;  and  as  it  is  these  qualities  which  we  can  most  conven- 
iently regard  as  being  immediately  adjustable  in  any  arbitrary 
manner,  we  shall  generally  consider  them  as  the  independent 
variables  in  formulas  expressing  the  pressure,  the  specific  heats, 
and  other  properties  of  the  particular  fluid  in  any  physical  con- 
dition. 

Let  v  be  the  volume  (in  cubic  feet)  of  a  unit  mass  (one 
pound)  of  the  fluid,  and  t  its  absolute  temperature  ;  and  let  p 
be  its  pressure  in  the  condition  defined  by  these  elements. 

Let  also  e  be  the  " mechanical  energy"*  of  the  fluid,  reck- 
oned from  some  assumed  standard  or  zero  state,  that  is,  the 
sum  of  the  mechanical  value  of  the  heat  communicated  to  it, 
and  of  the  work  spent  on  it,  to  raise  it  from  that  zero  state  to 
the  condition  defined  by  (v,  t) ;  and  let  N  and  K  be  its  specific 
heats  with  constant  volume,  and  with  constant  pressure,  respec- 
tively. Then,  denoting,  as  before,  the  mechanical  equivalent  of 
the  thermal  unit  by  J,  and  the  value  of  Carnot's  function  for 
the  temperature  t  by  /u,  we  havef 

de      3  dp 


dp 
de      1  /  de  •      \     dt 


dv 
From  these  we  deduce  by  eliminating  e, 


dp 
dv 


and 


*  Dynamical  Theory  of  Heat,  Part  V.,  On  the  Quantities  of  Mechanical 
Energy  Contained  in  a  Fluid  in  Different  States  as  to  Temperature  and 
Density,  §  82,  Trans.  Roy.  Soc.  Edin.,  Dec.  15,  1851. 

t  Ibid.,  §§  89,  91. 

77 


MEMOIRS     ON     THE 


i 


c/y  <#  J  dt 

equations  which  express  two  general  theorems  regarding  the 
specific  heats  of  any  fluid  whatever,  first  published*  in  the 
Transactions  of  the  Royal  Society  of  Edinburgh,  March,  1851. 
The  former  (4)  is  the  extension  of  a  theorem  on  the  specific 
heats  of  gases  originally  given  by  Carnot,f  while  the  latter  (5) 
is  inconsistent  with  one  of  his  fundamental  assumptions,  and 
expresses,  in  fact,  the  opposed  axiom  of  the  Dynamical  Theory. 
The  use  of  the  absolute  thermodynamic  system  of  thermome- 
try  proposed  in  Section  IV.,  according  to  which  the  definition 
of  temperature  is 


simplifies  these  equations,  and  they  become 


dp 
dv 


To  compare  with  the  absolute  scale  the  indications  of  a  ther- 
mometer in  which  the  particular  fluid  (which  may  be  any  gas, 
or  even  liquid)  referred  to  in  the  notation  p,  v,  t  is  used  as 
the  thermometric  substance,  let  pQ  and^?100  denote  the  pressures 
which  it  has  when  at  the  freezing  and  boiling  points  respective- 
ly, and  kept  in  constant  volume,  v  ;  and  let  VQ  and  vloo  denote 
the  volumes  which  it  occupies  under  the  same  pressure,  p,  at 
those  temperatures.  Then  if  0  and  $  denote  its  thermometric 

*  Dynamical  Theory  of  Heat,  Part  V.,  On  the  Quantities  of  Mechanical 
Energy  Contained  in  a  Fluid  in  Different  States  as  to  Temperature  and 
Density,  §§  47,  48. 

f  See  "Account  of  Carnot's  Theory,"  Appendix  III.,  Trans.  Roy.  Soc. 
Edin.,  April  30,  1849,  p.  565. 

78 


FREE    EXPANSION    OF    GASES 

indications  when  used  as  a  constant-volume  and  as  a  constant- 
pressure  thermometer  respectively,  we  have 

0  =  100   ^~^°        (9) 

(10) 


Let  also  s  denote  the  "  coefficient  of  increase  of  elasticity  with 
temperature/'  *  and  c  denote  the  coefficient  of  expansion  at 
constant  pressure,  when  the  gas  is  in  the  state  defined  by  (v,  £); 
and  let  Eand  ^denote  the  mean  values  of  the  same  coefficients 
between  0°  and  100°  Cent.  Then  we  have 

E=A| .     (n) 

dp 

*  (») 


dp 

£t          XX      L- 

dv 

E=Plw-Po 

E=V-1 


lOOv 


Lastly,  the  general  expression  for-,  quoted  in  Section  II.  from 

our  paper  of  last  year,  leads  to  the  following  expression  for  the 
cooling  effect  on  the  fluid  when  forced  through  a  porous  plug 
as  in  our  air  experiments  : 


(p,  v),  (P',V),  (P,V),  as  explained  above,  having  reference  to 
the  fluid  in  different  states  of  density,  but  always  at  the  same 
temperature,  t,  as  that  with  which  it  enters  the  plug. 

*  So  called  by  Mr.  Rankine.    The  same  element  is  called  by  M.  Regnault 
the  coefficient  of  dilatation  of  a  gas  at  constant  volume. 

79 


MEMOIRS    ON    THE 

From  these  equations  it  appears  that  if  p  be  fully  given  in 
terms  of  v  and  absolute  values  for  t  for  any  fluid,  the  various 
properties  denoted  by 


JK-  JN,  -,  0,  S,  e,  e,  E,  E,  and  3 

may  all  be  determined  for  it  in  every  condition.  Conversely, 
experimental  investigations  of  these  properties  may  be  made  to 
contribute,  along  with  direct  measurements  of  the  pressure  for 
various  particular  conditions  of  the  fluid,  towards  completing 
the  determination  of  the  function  which  expresses  this  element 
in  terms  of  v  and  t.  But  it  must  be  remarked  that  even  com- 
plete observations  determining  the  pressure  for  every  given 
state  of  the  fluid  could  give  no  information  as  to  the  values  of 
t  on  the  absolute  scale,  although  they  might  afford  data  enough 
for  fully  expressing  jo  in  terms  of  the  volume  and  the  tempera- 
ture with  reference  to  some  particular  substance  used  ther- 
mometrically.  On  the  other  hand,  observations  on  the  specific 
heats  of  the  fluid,  or  on  the  thermal  effects  it  experiences  in 
escaping  through  narrow  passages,  may  lead  to  a  knowledge  of 
the  absolute  temperature,  t,  of  the  fluid  when  in  some  known 
condition,  or  to  the  expression  of  p  in  terms  of  v,  and  absolute 
values  of  t  ;  and  accordingly  the  formulae  (7),  (8),  and  (15) 
contain  t  explicitly,  each  of  them,  in  fact,  essentially  involving 
Carnot's  function.  As  for  actual  observations  on  the  specific 
heats  of  air,  none  which  have  yet  been  published  appear  to 
do  more  than  illustrate  the  theory,  by  confirming  (as  Mr. 
Joule's,  and  the  more  precise  results  more  recently  published 
by  M.  Regnault,  do),  within  the  limits  of  their  accuracy,  the 
value  for  the  specific  heat  of  air  under  constant  pressure  which 
we  calculated*  from  the  ratio  of  the  specific  heats,  determined 
according  to  Laplace's  theory  by  observations  on  the  velocity 
of  sound,  and  the  difference  of  the  specific  heats  determined  by 
Carnot's  theorem  with  the  value  of  Carnot's  function  estimated 
from  Mr.  Joule's  original  experiments  on  the  changes  of  tem- 
perature produced  by  the  rarefaction  and  condensation  of  airf 
and  established  to  a  closer  degree  of  accuracy  by  our  prelimi- 
nary experiments  on  expansion  through  a  resisting  solid.  J  It 

*  Philosophical  Transactions,  March,  1852,  p.  82. 
f  Royal  Society  Proceedings,  June  20,  1844  ;  or  Phil.  Mag.,  May,  1845. 
.,  December,  1850. 

80 


FREE    EXPANSION     OF    GASES 

ought  also  to  be  remarked  that  the  specific  heats  of  air  can  only 
be  applied  to  the  evaluation  of  absolute  temperature  with  a 
knowledge  of  the  mechanical  equivalent  of  the  thermal  unit ; 
and,  therefore,  it  is  probable  that,  even  when  sufficiently  accu- 
rate determinations  of  the  specific  heats  are  obtained,  they  may 
be  useful  rather  for  a  correction  or  verification  of  the  mechan- 
ical equivalent  than  for  the  thermometric  object.  On  the 
other  hand,  a  comparatively  very  rough  approximation  to  JK, 
the  mechanical  value  of  the  specific  heat  of  a  pound  of  the 
fluid,  will  be  quite  sufficient  to  render  our  experiments  on  the 
cooling  effects  available  for  expressing  with  much  accuracy  by 
means  of  the  formula  (15)  a  thermodynamic  relation  between 
absolute  temperature  and  the  mechanical  properties  of  the  fluid 
at  two  different  temperatures. 

In  the  notes  to  Mr.  Joule's  paper  on  the  Air-Engine,*  it  was 
shown  that  if  Mayer's  hypothesis  be  true  we  must  have  approx- 
imately, 

K  =  .2374  and  N  =  .1684, 

because  observations  on  the  velocity  of  sound,  with  Laplace's 
theory,  demonstrate  that 

k=  1.410, 

within  y^-g-  of  its  own  value.  Now  the  experiments  at  present 
communicated  to  the  Royal  Society  prove  a  very  remarkable 
approximation  to  the  truth  in  that  hypothesis  (see  above,  Sec- 
tion I.),  and  we  may  therefore  use  these  values  as  very  close 
approximations  to  the  specific  heats  of  air.  The  experiments 
on  the  friction  of  fluids  and  solids  made  for  determining  the 
mechanical  value  of  heatf  give  for  J  the  value  1390  ;  and  we 
therefore  have  JN  =  234.1  with  sufficient  accuracy  for  use  in 
calculating  small  terms. 

Now,  according  to  Regnault,  we  have,  for  dry  air  at  the 
freezing-point,  in  the  latitude  of  Paris, 

H  =  26215  ; 

and  since  the  force  of  gravity  at  Paris,  with  reference  to  a  foot 
as  the  unit  of  space  and  a  second  as  the  unit  of  time,  is  32.1813, 

*  Philosophical  Transactions,  March,  1852   p  82 
t  Ibid.,  1849. 
F  81 


FREE     EXPANSION     OF    GASES 

it  follows  that  the  velocity  of  sound  in  dry  air  at  0°   Cent. 
would  be,  according  to  Newton's  unmodified  theory, 


X  32.1813  =  918.49  ; 
or,  in  reality,  according  to  Laplace's  theory, 

Vk  -V/26215  X  32.1813. 
But  according  to  Bravais  and  Martins  it  is  in  reality 

1090.5,  which  requires  that  k  =  1.4096  ; 
or,  according  to  Moll  and  Van  Beck, 

1090.1,  which  requires  that  k  =  1.4086. 
The  mean  of  these  values  of  k  is  1.4091. 


[Note  of  January  5,  1882,  by  Sir  W.  Thomson.— That  portion  of  this 
Second  Part  of  our  researches  which  was  devoted  to  working  out  an  em- 
pirical formula  for  the  thermo-elastic  properties  of  air,  and  the  calculation 
of  specific  heats  from  it,  is  not  reproduced  here,  because  at  the  conclusion 
of  Part  IV.  we  have  derived  a  better  and  simpler  empirical  formula  from 
more  comprehensive  experimental  data.] 


ABSTRACT  OF  THE  ABOVE  PAPER  "ON  THE  THERMAL  EFFECTS 
OF  FLUIDS  IK  MOTION." 

No.  II. 

BY  J.    P.    JOULE,   ESQ.,  F.R.S.,  AND  PROFESSOR  W.  THOMSON, 
F.R.S.     (Proceedings  of  the  Royal  Society,  Vol.  VII.,  p.  127.) 

THE  first  experiments  described  in  this  paper  show  that  the 
anomalies  exhibited  in  the  last  table  of  experiments,  in  the 
paper  preceding  it,*  are  due  to  fluctuations  of  temperature  in 
the  issuing  stream  consequent  on  a  change  of  the  pressure  with 
which  the  entering  air  is  forced  into  the  plug.  It  appears  from 
these  experiments  that  when  a  considerable  alteration  is  sud- 
denly made  in  the  pressure  of  the  entering  stream,  the  issuing 
stream  experiences  remarkable  successions  of  augmentations 
and  diminutions  of  temperature,  which  are  sometimes  percep- 
tible for  half  an  hour  after  the  pressure  of  the  entering  stream 
has  ceased  to  vary. 

Several  series  of  experiments  are  next  described  in  which  air 
is  forced  (by  means  of  a  large  pump  and  other  apparatus  de- 
scribed in  the  first  paper)  through  a  plug  of  cotton-wool,  or 
unspun  silk  pressed  together,  at  pressures  varying  in  their  ex- 
cess above  the  atmospheric  pressure  from  five  or  six  up  to 
fifty  or  sixty  pounds  on  the  square  inch.  By  these  it  appears 
that  the  cooling  effect  which  the  air,  as  found  in  the  authors 
previous  experiments,  always  experiences  in  passing  through 
the  porous  plug,  varies  proportionally  to  the  excess  of  pressure 
of  the  air  on  entering  the  plug  above  that  with  which  it  is 
allowed  to  escape.  Seven  series  of  experiments,  in  each  of 
which  the  air  entered  the  plug  at  a  temperature  of  about  16° 
Cent.,  gave  a  mean  cooling  effect  of  about  0°.0175  Cent,  per 
pound  on  the  square  inch,  orO°.27  Cent,  per  atmosphere  of  dif- 

*Proc.  Roy.  Soc.,  and  Phil.  Mag.,  September,  1853,  p.  230. 
83 


MEMOIRS     ON     THE 

ference  of  pressure.  Experiments  made  at  lower  and  at  higher 
temperatures  showed  that  the  cooling  effect  is  very  sensibly 
less  for  high  than  for  low  temperatures,  but  have  not  yet  led 
to  sufficiently  exact  results  at  other  temperatures  than  that 
stated  (16°  Cent.)  to  indicate  the  law  according  to  which  it 
varies  with  the  temperature. 

Experiments  on  carbonic  acid  at  different  temperatures  are 
also  described,  which  show  that  at  about  16°  Cent,  this  gas  ex- 
periences 4£  times  as  great  a  cooling  effect  as  air.  They  agree 
well  at  all  the  different  temperatures  with  a  theoretical  result, 
derived  according  to  the  general  dynamical  theory  from  empir- 
ical formulae  for  the  pressure  of  carbonic  acid  in  terms  of  its 
temperature  and  density,  which  was  kindly  communicated  by 
Mr.  Rankine  to  the  authors,  having  been  investigated  by  him 
upon  no  other  experimental  data  than  those  of  Regnault  on 
the  expansion  of  gas  by  heat  and  its  compressibility. 

Experiments  were  also  made  on  hydrogen  gas,  which,  al- 
though not  such  as  to  lead  to  accurate  determinations,  appeared 
to  indicate  very  decidedly  a  cooling  effect*  amounting  to  a  small 
fraction,  perhaps  about  ^  of  that  which  air  would  experience 
in  the  same  circumstances. 

The  following  theoretical  deductions  from  these  experiments 
are  made : 

I.  The  relations  between  the  heat  generated  and  the  work 
spent  in  compressing  carbonic  acid,  air,  and  hydrogen,  are  in- 
vestigated from  the  experimental  results.     In  each  case  the 
relation  is  nearly  that  of  equivalence,  but  the  heat  developed 
exceeds  the  equivalent  of  the  work  spent   by   a   very   small 
amount  for  hydrogen,  considerably  more  for  air,  and  still  more 
for  carbonic  acid.     For  slight  compressions  with  the  gases  kept 
about  the  temperature  16°,  this  excess  amounts  to  about  -f^  of 
the  whole  heat  emitted  in  the  case  of  carbonic  acid  and  %fc  in 
the  case  of  air. 

II.  It  is  shown  in  the  general  dynamical  theory  that  the  air 
experiments  taken  in  connection  with  Regnault's  experimen- 
tal results  on  the  latent  heat  and  pressure  of  saturated  steam 
make  it  certain  that  the  density  of  saturated  steam  increases 
very  much  more  with  the  pressure  than  according  to  Boyle's 
and  Gay-Lussac's  gaseous  laws,  and  numbers  are  given  express- 

[*  Later  experiments  showed  this  to  be  a  mistake.     See  Part  /F.] 

84 


FREE    EXPANSION    OF    GASES 

ing  the  theoretical  densities  of  saturated  steam,  at  different 
temperatures,  which  it  is  desired  should  be  verified  by  direct 
experiments. 

III.  Carnot's  function  in  the  "  Theory  of  the  Motive  Power 
of  Heat"  is  shown  to  be  very  nearly  equal  to  the  mechanical 
equivalent  of  the  thermal  unit  divided  by  the  temperature  from 
the  zero  of  the  air-thermometer  (that  is,  temperature  Centi- 
grade with  a  number  equal  to  the  reciprocal  of  the  coefficient 
of  expansion  added),  and  corrections,  depending  on  the  amount 
of  the  observed  cooling  effects  in  the  new  air  experiments,  and 
the  deviations  from  the  gaseous  laws  of  expansion  and  com- 
pression determined  by  Kegnault,  are  applied  to  give  a  more 
precise  evaluation. 

IV.  An  absolute  scale  of  temperature — that  is,  a  scale  not 
founded  on  reference  to  any  particular  thermornetric  substance 
or  to  any  special  qualities  of  any  class  of  bodies — is  founded  on 
the  following  definition  : 

If  a  physical  system  be  subjected  to  cycles  of  perfectly  reversible 
operations  and  be  not  allowed  to  take,  in  or  emit  heat  except  in 
localities,  at  two  fixed  temperatures,  these  temperatures  are  pro- 
portional to  the  whole  quantities  of  heat  taken  in  or  emitted  at 
them  respectively  during  a  complete  cycle  of  the  operations. 

The  principles  upon  which  the  degree  or  unit  of  temperature 
is  to  be  chosen,  so  as  to  make  the  difference  of  temperatures  on 
the  absolute  scale  agree  with  that  on  any  other  scale  for  a  par- 
ticular range  of  temperatures.  If  the  difference  of  tempera- 
tures between  the  freezing-  and  the  boiling-points  of  water  be 
made  100°  on  the  new  scale,  the  absolute  temperature  of  the 
freezing-point  is  shown  to  be  about  273°.  7;  and  it  is  demon- 
strated that  the  temperatures  from  the  freezing-point  on  the 
new  scale  will  agree  very  closely  with  Centigrade  temperature 
by  the  standard  air-thermometer;  quite  within  the  limits  of 
the  most  accurate  practical  thermometry  when  the  temperature 
is  between  0°  and  100°  Cent.,  and  very  nearly,  if  not  quite, 
within  these  limits  for  temperatures  up  to  300°  Cent. 

[V.  An  empirical  formula  for  the  pressure  of  air  in  terms  of 
its  density,  and  its  temperature  on  the  absolute  scale,  is  inves- 
tigated by  using  forms  such  as  those  first  proposed  and  used 
by  Mr.  Rankine,  and  determining  the  constants  so  as  to  fulfil 

85 


FREE    EXPANSION    OF    GASES 

the  conditions  (1)  of  giving  the  observed  cooling  effects,  (2)  of 
agreeing  with  Regnault's  experimental  results  on  compressi- 
bility at  a  particular  temperature. 

A  table  of  comparison  of  temperature  by  the  air-thermom- 
eter under  varied  conditions  of  temperature  and  pressure  with 
the  absolute  scale  is  deduced  from  this  formula.]* 

Expressions  for  the  specific  heat  of  any  fluid  in  terms  of 
the  absolute  temperature,  the  density,  and  the  pressure,  derived 
from  the  general  dynamical  theory,  are  worked  out  for  the  case 
of  air  according  to  the  empirical  formula ;  and  tables  of  numer- 
ical results  derived  exclusively  from  these  expressions  and  the 
ratio  of  the  specific  heats  as  determined  by  the  theory  of  sound 
are  given.  These  tables  show  the  mechanical  values  of  the  spe- 
cific heats  of  air  at  different  constant  pressures  and  at  con- 
stant densities.  Taking  1390  as  the  mechanical  equivalent  of 
the  thermal  unit  as  determined  by  Mr.  Joule's  experiment  on 
the  friction  of  fluids,  the  authors  find,  as  the  mean  specific 
heat  of  air  under  constant  pressure, 

0.2390,  from  0°  to  100°  Cent. 
0.2384,  from  0°  to  300°  Cent. 

*  [The  section  in  brackets  appears  in  tlie  original  contribution  to  the  Proc. 
Roy.  Soc.  and  in  Thomson's  Math,  and  Phys.  Papers,  but  is  omitted  in 
.  Joule's  Scientific  Papers. ] 


Ox  THE  THERMAL  EFFECTS  OF  FLUIDS  IN  MOTIOX. 
PART  IV. 

BY   J.   P.  JOULE,   LL.D.,   F.R.S.,   ETC.,   AND  PROFESSOR 
WILLIAM  THOMSON,  A.M.,  LL.D.,  F.R.S.,  ETC. 

(Phil.  Trans.,  1862,  p.  579.) 

IN  the  Second  Part  of  these  researches  we  have  given  the 
results  of  our  experiments  on  the  difference  between  the  tem- 
peratures of  an  elastic  fluid  on  the  high-  and  low-pressure  sides 
of  a  porous  plug  through  which  it  was  transmitted.  The  gases 
employed  were  atmospheric  air  and  carbonic  acid.  With  the 
former  0°.0176  of  cooling  effect  was  observed  for  each  pound 
per  square  inch  of  difference  of  pressure,  the  temperature  on 
the  high -pressure  side  being  17°.  125.  With  the  latter  gas 
0°.0833  of  cooling  effect  was  produced  per  pound  of  difference 
of  pressure,  the  temperature  on  the  high-pressure  side  being 
12°.  844. 

It  was  also  shown  that  in  each  of  the  above  gases  the  differ- 
ence of  the  temperatures  on  the  opposite  sides  of  the  porous 
plug  is  sensibly  proportional  to  the  difference  of  the  pressures. 

An  attempt  was  also  made  to  ascertain  the  cooling  effect 
when  elastic  fluids  of  high  temperatures  were  employed ;  and 
it  was  satisfactorily  shown  that  in  this  case  a  considerable 
diminution  of  the  effect  took  place.  Thus,  in  air  at  91°. 58 
the  effect  was  only  0°.014 ;  and  in  carbonic  acid  at  91°. 52  it 
was  0°.0474. 

In  the  experiments  at  high  temperature  there  appeared  to  be 
some  grounds  for  suspecting  that  the  apparent  cooling  effect 
was  too  high  ;  for  the  quantity  of  transmitted  air  was  very  con- 
siderable, and  its  temperature  had  possibly  not  arrived  accu- 
rately at  that  of  the  bath  by  the  time  it  reached  the  porous 
plug. 

87 


MEMOIRS    ON    THE 

The  obvious  way  to  get  rid  of  all  uncertainty  on  this  head 
was  to  increase  the  length  of  the  coil  of  pipes.  Hence  in  the 
following  experiments  the  total  length  of  2-inch  copper  pipe 
immersed  in  the  bath  was  60  feet,  instead  of  35,  as  in  the  former 
series.  The  volume  of  air  transmitted  in  a  given  time  was  also 
considerably  less.  There  could,  therefore,  be  no  doubt  that 
the  temperature  of  the  air  on  its  arrival  at  the  plug  was  sensi- 
bly the  same  as  that  of  the  bath. 

The  nozzle  employed  in  the  former  series  of  experiments 
was  of  boxwood — the  space  occupied  by  cotton-wool,  or  other 
porous  material,  being  2.72  inches  long  and  an  inch  and  a  half 
in  diameter.  The  boxwood  was  protected  from  the  water  of 
the  bath  by  being  enveloped  by  a  tin  can  filled  with  cotton- 
wool. This  was  unquestionably  in  most  respects  the  best  ar- 
rangement for  obtaining  accurate  results ;  but  it  was  found 
necessary  to  make  each  experiment  last  one  hour  or  more  be- 
fore we  could  confidently  depend  on  the  thermal  effect.  The 
oscillations  of  temperature  which  took  place  during  the  first 
part  of  the  time  were  traced  to  various  causes,  one  of  the  prin- 
cipal being  the  length  of  time  which,  on  account  of  the  large 
capacity  for  heat  and  the  small  conductivity  of  the  boxwood 
nozzle,  elapsed  before  the  first  large  thermal  effects  consequent 
on  the  getting  up  of  the  pressure  were  dissipated.  No  doubt 
the  results  we  arrived  at  were  very  accurate  with  the  elastic 
fluids  employed,  viz.,  atmospheric  air  and  carbonic  acid;  but 
we  possessed  an  unlimited  supply  of  the  former  and  a  supply 
of  the  latter  equal  to  120  cubic  feet,  which  was  sufficient  to 
last  for  more  than  half  an  hour  without  being  exhausted.  In 
extending  the  inquiry  to  gases  not  so  readily  procured  in  large 
quantities,  it  was  therefore  desirable  to  use  a  porous  plug  of 
smaller  dimensions  enclosed  in  a  nozzle  of  less  capacity  for 
heat,  so  as  to  arrive  rapidly  at  the  normal  effect. 

Various  alterations  of  the  apparatus  were  made  in  order  to 
meet  the  requirements  of  our  experiments.  A  small  high- 
pressure  engine  of  about  one  horse-power  was  placed  in  gear 
with  a  double-acting  compressing  air-pump,  which  had  a  cylin- 
der four  and  a  half  inches  in  diameter,  with  a  length  of  stroke 
of  nine  inches.  The  engine  was  able  to  work  the  piston  of  the 
pump  sixty  complete  strokes  in  the  minute.  The  quantity  of 
air  which  it  ought  to  have  discharged  at  low  pressure  was 
therefore  upwards  of  16,000  cubic  inches  per  minute.  But 


FREE    EXPANSION    OF    GASES 
PLATE  III.— FIG.  1. 


a 


MEMOIRS    ON    THE 

much  loss,  of  course,  occurred  from  leakage  past  the  metallic 
piston,  and  in  consequence  of  the  necessary  clearance  at  the  top 
and  bottom  of  the  cylinder  when  the  pressure  increased  by  a 
few  atmospheres  ;  so  that  in  practice  we  never  pumped  more 
than  8000  cubic  inches  per  minute. 

The  nozzle  we  employed  will  be  understood  by  inspecting 
Plate  III.,  Fig.  1,  where  a  a  is  the  upright  end  of  the  coil  of 
copper  pipes.  On  the  shoulder  within  the  pipe  a  perforated 
metallic  disk  (b)  rests.  Over  this  is  a  short  piece  of  india- 
rubber  tube  (c  c)  enclosing  a  silk  plug  (d),  which  is  kept  in 
a  compressed  state  by  the  upper  perforated  metallic  plate  (e). 
This  upper  plate  is  pressed  down  with  any  required  force  by 
the  operation  of  the  screw/  on  the  metallic  tube  g  g.  A  tube 
of  cork  (h  h]  is  placed  within  the  metallic  tube,  in  order  to 
protect  the  bulb  of  the  thermometer  from  the  effects  of  a  too 
rapid  conduction  of  heat  from  the  bath.  Cotton -wool  is 
loosely  packed  round  the  bulb,  so  as  to  distribute  the  flowing 
air  as  evenly  as  possible.  The  glass  tube  (/  i)  is  attached  to 
the  nozzle  by  means  of  a  strong  piece  of  india-rubber  tubing 
\JcJc\t  and  through  it  the  indications  of  the  thermometer  are 
read.  The  top  of  the  glass  tube  is  attached  to  the  metallic 
tube  1 1,  for  the  purpose  of  conveying  the  gas  to  the  meter. 

The  thermometer  (m)  for  registering  the  temperature  of  the 
bath  is  placed  with  its  bulb  near  the  nozzle.  Tne  level  of  the 
water  is  shown  by  n  n ;  and  o  o  represents  the  wooden  cover 
of  the  bath.  When  a  high  temperature  was  employed  it  was 
maintained  by  introducing  steam  into  the  bath  by  means  of  a 
pipe  led  from  the  boiler.  The  water  of  the  bath  was  in  every 
case  constantly  and  thoroughly  stirred,  especially  when  high 
temperatures  were  used. 

The  general  disposition  of  the  apparatus  will  be  understood 
from  Fig. -2,  in  which  A  represents  the  boiler,  B  the  steam- 
engine  geared  to  the  condensing  air  -  pump  C.  From  this 
pump  the  compressed  air  passes  through  a  train  of  pipes  60 
feet  long  and  2  inches  in  diameter,  and  then  enters  the  coil  of 
pipes  Jh  the  bath  D.  Thence,  after  issuing  from  the  porous 
plug,  it  passes  through  the  gasometer  E,  and  ultimately  arrives 
again  at  the  pump  C.  This  complete  circulation  is  of  great 
importance,  inasmuch  as  it  permits  the  gas  which  has  been  col- 
lected in  the  meter  to  be  used  for  a  much  longer  period  than 
would  otherwise  have  been  possible.  A  glass  vessel  full  of 

90 


FREE     EXPANSION     OF     GASES 
FIG.  2. 


MEMOIRS     ON     THE 

chloride  of  calcium  is  also  placed  in  the  pipe  at/.  A  small 
tube  leading  from  the  coil  is  carried  to  the  shorter  leg  of  the 
glass  siphon  gauge  G,  of  which  the  longer  leg  is  17  feet  and 
the  shorter  12  feet  long. 

The  thermometers  employed  were  all  carefully  calibrated,  and 
had  about  ten  divisions  to  the  degree  Centigrade.  We  took  the 
precaution  of  verifying  the  air-  and  bath-thermometers  from 
time  to  time,  especially  when  high  temperatures  were  used,  in 
which  latter  case  a  comparison  between  the  thermometers  at 
high  temperature  was  made  immediately  after  each  experiment. 

Atmospheric  Air.     (See  Table  I.) 

In  the  experiments  described  in  the  present  paper  the  air  was 
not  deprived  of  its  carbonic  acid.  It  was  simply  dried  by  trans- 
mitting it  in  the  first  place,  before  it  entered  the  pump,  through 
a  cylinder  18  inches  long  and  12  inches  in  diameter  filled  with 
chloride  of  calcium,  and  afterwards,  in  its  compressed  state, 
through  a  pipe  12  feet  long  and  2  inches  in  diameter  filled  with 
the  same  substance.  The  experiments  were  principally  carried 
on  in  the  winter  season  ;  so  that  the  chloride  kept  dry  for  a 
long  time.  From  its  condition  after  some  weeks'  use,  it  was 
evident  that  the  water  was  removed,  almost  as  much  as  chlo- 
ride of  calcium  can  remove  it,  after  the  air  had  traversed  three 
inches  of  the  chloride  contained  by  the  first  vessel. 

Oxygen  Gas.     (See  Table  II.) 

This  elastic  fluid  was  procured  by  cautiously  heating  chlo- 
rate of  potash  mixed  with  a  small  quantity  of  peroxide  of  man- 
ganese. In  its  way  to  the  meter  it  passed  through  a  tube  con- 
taining caustic  potash,  in  order  to  deprive  it  of  any  carbonic 
acid  it  might  contain.  The  same  drying  apparatus  was  em- 
ployed as  in  the  case  of  atmospheric  air. 

Nitrogen  Gas.     (See  Table  III.) 

In  preparing  this  gas  the  meter  was  first  filled  with  air,  and 
then  a  long,  shallow  tin  vessel  was  floated  under  it,  containing 
sticks  of  phosphorus  so  disposed  as  to  burn  in  succession. 
Some  hours  were  allowed  to  elapse  after  the  combustion  had 
terminated,  in  order  to  allow  of  the  deposition  of  phosphoric 
acid  formed. 

93 


FREE    EXPANSION     OF    GASES 


No.  of  Experiment 


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OT  O  CO  to  -Q 


Cubical  Inches  of 

Air  Transmitted 

per  Minute 


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Pressure  over 
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Atmosphere,  in 
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Temperature  of 
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Time  Occupied  by 

Experiment,  in 

Minutes 


I 

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Number  of  Obser- 
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Extreme  Range 
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Extreme  Range  of 
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Carbonic  Add.     (See  Table  IV.) 

This  gas  was  formed  by  adding  sulphuric  acid  to  a  solution 
of  carbonate  of  soda.  It  was  dried  in  the  same  manner  as  all 
the  other  gases. 

Hydrogen.     (See  Table  V.) 

Our  method  of  procuring  this  elastic  fluid  was  to  pour  sul- 
phuric acid,  prepared  from  sulphur,  into  a  carboy  nearly  filled 
with  water  and  containing  fragments  of  sheet  zinc.  The  gas 
was  passed  through  a  tube  filled  with  rags  steeped  in  a  solution 
of  sulphate  of  copper,  and  then  through  a  tube  filled  with 
sticks  of  caustic  potash.  The  rags  became  speedily  browned, 
and  we  therefore  adopted  the  plan  of  pouring  a  small  quantity 
of  solution  of  sulphate  of  copper  from  time  to  time  into  the 
carboy  itself.  This  succeeded  perfectly ;  the  rags  retained 
their  blue  color,  and  the  gas  was  rendered  perfectly  inodorous, 
while  at  the  same  time  its  evolution  became  much  more  free 
and  regular. 


MEMOIRS    ON    THE 


£4 


Q       <M 

5  I 


si! 


2 

O      2 
£-     *J 

w  ^ 


FREE    EXPANSION    OF    GASES 


Remarks  on  the  Tables. 

The  correction  of  conduction  of  heat  through  the  plug, 
inserted  in  column  6  of  Table  I., -and  in  column  7  of  the  rest 
of  the  Tables,  was  obtained  from  data  furnished  by  experiments 
in  which  the  difference  between  the  temperature  of  the  bath 
and  the  air  was  purposely  made  very  great.  It  was  considered 
as  directly  proportional  to  the  difference  of  temperature, 
and  inversely  to  the  quantity  of  elastic  fluid  transmitted  in  a 
given  time. 

The  10th  column  of  Tables  II.,  III.,  IV.,  and  V.  is  calculated 
on  the  hypothesis  that,  in  mixtures  with  other  gases,  atmos- 
pheric air  retains  its  thermal  qualities  without  change.  This 
hypothesis  is  almost  certainly  incorrect,  since  it  is  reasonable 
to  expect  that  the  effect  of  mixture  on  the  physical  character 
is  experienced  by  each  of  the  constituent  gases.  The  column 
is  given  as  one  method  of  showing  the  effect  of  mixture. 

Effect  of  Mixture  on  the  Constituent  Gases.  —  Although  the 
experiments  on  nitrogen  given  in  Table  III.  are  not  so  numer- 
ous as  might  be  desired,  we  may  infer  from  them,  and  the  re- 
sults in  Table  II.,  that  common  air  and  all  other  mixtures  of 
nitrogen  and  oxygen  behave  more  like  a  perfect  gas,  i.  e.,  give 
less  cooling  effect  than  either  one  or  the  other  gas  alone.  We 
might  expect  the  mixture  to  be  something  intermediate  be- 
tween the  two.  But  this  does  not  appear  to  be  the  case.  The 
two  are  very  nearly  equal  in  their  deviations  from  the  condi- 
tion of  a  perfect  gas.  Nitrogen  deviates  less  than  oxygen,  but 
oxygen  mixed  with  nitrogen  differs  less  than  nitrogen  ! 

In  the  case  of  carbonic  acid,  which  at  low  temperatures  (7°) 
deviates  five  times  as  much  as  atmospheric  air,  we  migh^  ex- 
pect that  a  mixture  of  C02  and  air  would  deviate  more  than 
air  and  less  than  C02.  This  is  the  case  (see  Table  IV.). 
Further,  we  might  expect  the  two  to  contribute  each  its  own 
proportion  of  cooling  effect  according  to  its  own  amount,  and 
its  specific  heat  volume  for  volume.  But  do  the  mixtures  ex- 
hibit such  a  result  ?  No  !  See  column  10,  Table  IV.,  in 
which  also  note,  under  experiments  8  and  9,  the  great  diminu- 
ation  produced  by  the  admixture  of  hydrogen.  . 

If,  instead  of  attributing  to  air  and  carbonic  acid  moments 
in  proportion  to  their  specific  heats,  or  1  :  1.39,  as  we  have 

99 


MEMOIRS    ON    THE 

done  in  column  10,  we  use  1  :  .7,  we  obtain  more  consistent 
results. 

Let  3  denote  the  cooling  effect  experienced  by  air  per  100 
inches  mercury,  3'  that  by  carbonic  acid,  and  A  that  by  a  mixt- 
ure of  volume  V  of  air,  and  V  of  carbonic  acid  ;  then  we  may 
take 

4-  w'V'S' 


A  = 


raV+m'V 


to  represent  the  cooling  effect  for  the  mixture,  where  m  and  m' 
are  numbers  which  we  may  call  the  moments  (or  importances) 
of  the  two  in  determining  the  cooling  effect  for  the  mixture. 
The  ratio  of  m  to  m'  is  the  proper  result  of  each  experiment  on 
a  mixture,  if  we  knew  with  perfect  accuracy  the  cooling  effect 
for  each  gas  with  none  of  the  other  mixed.  Now,  for  common 
air  we  have  direct  experiments  (Table  I.),  and  know  the  cooling 
effect  for  it  better  than  from  any  inferences  from  mixtures. 
But  for  pure  C02  we  know  the  effect  for  the  most  part  only 
inferentially.  Hence,  having  tried  making  m  :  m'  ::  1  :  1.39 
without  obtaining  consistent  results,  we  tried  other  propor- 
tions, and,  after  various  attempts,  found  that  m:m'  ::  1  :  .7, 
for  ail  temperatures  and  pressures  within  the  limits  of  our  ex- 
periments, gives  results  as  consistent  with  one  another  as  the 
probable  errors  of  the  experiments  justify  us  in  expecting. 
Thus,  using  the  formula 

va+va'x.7 

V+V'x.7  ' 

we  have,  for  calculating  the  effect  of  C02  from  any  experiment 
on  a  mixture,  the  following  formula, 

y_  (V  +  V'x.7)  A -VS 
V'x.7 

Hence,  using  the  numbers  in  columns  3  and  9  of  Table  IV., 
which  relate  to  mixtures  of  air  and  carbonic  acid  alone,  we 
find: 


FREE    EXPANSION    OF    GASES 


TABLE  VI. 


No.  of  Ex- 
periment 

Proportions  of 
Mixtures 

Temperature 
of  Bath 

Thermal  Effect 
for  Air 

Deduced  Thermal 
Eflect  for  Pure 
C02 

Air                C02 

Q 

0 

o 

1 

68.42        31.58 

7.36 

-.88 

-4.51 

2 

89.16        10.84 

7.36 

-.88 

-4.61 

3 

3.52        96.48 

7.38 

-.88 

-446 

4 

62.5          37.5 

7.41 

-.88 

-4.19 

5 

88.13        11.87 

7.43 

-.88 

-3.98 

6 

97.46          2.54 

7.61 

-.88 

-3.89 

16 

1.83        98.17 

35.6 

-.75 

-3.44 

14 

67.7          32.3 

49.7 

-.70 

-3.04 

15 

87.77        12.23 

49.76 

-.70 

-2.77 

13 

0.83        99.17 

54 

-.66 

-2.96 

10 

2.11        97.89 

93.52 

-.51 

-2.19 

11 

56.78        43.22 

91.26 

-.51 

-2.21 

12 

77.77        22  23 

91.64 

-.51 

-3.08 

17 

1.66        9834 

97.55 

-.49 

-2.16 

1 

2 

3 

4 

5 

The  agreement  for  each  set  of  results  at  temperatures  nearly 
agreeing  (with  one  exception,  No.  12)  shows  that  the  assump- 
tion m:m  ::  1  :  .7  cannot  be  far  wrong  within  our  limits  of 
temperature. 

[For  continuation,  see  Thomson's  Papers,  Vol.  I.,  p.  Jf%7,  and 
Joule's  Scientific  Papers,  Vol.  II. ,  p.  357.  An  empirical  for- 
mula for  the  elasticity  of  gases  is  deduced.] 


ON  THE  THERMAL  EFFECTS  OF  FLUIDS  IN   MOTION. 
PART  IV. 

BY  J.  P.  JOULE,  LL.D  ,  F.R.S.,  AND  PROFESSOR  W.  THOMSON, 

A.M.,  F.R.S. 

(Abstract.     Pi'oceedings  of  the  Eoyal  Society,  Vol.  XII.,  p.  202.) 

A  BRIEF  notice  of  some  of  the  experiments  contained  in  this 
paper  has  already  appeared  in  the  Proceedings.  Their  object 
was  to  ascertain  with  accuracy  the  lowering  of  temperature, 
in  atmospheric  air  and  other  gases,  which  takes  place  on  pass- 
ing them  through  a  porous  plug  from  a  state  of  high  to  one  of 
low  pressure.  Various  pressures  were  employed,  with  the  re- 
sult (indicated  by  the  authors  in  their  Part  II.)  that  the  ther- 
mal effect  is  approximately  proportional  to  the  difference  of 
pressure  on  the  two  sides  of  the  plug.  The  experiments  were 
also  tried  at  various  temperatures,  ranging  from  5°  to  98°  Cent.; 
and  have  shown  that  the  thermal  effect,  if  one  of  cooling,  is 
approximately  proportional  to  the  inverse  square  of  the  abso- 
lute temperature.  Thus,  for  example,  the  refrigeration  at  the 
freezing  temperature  is  about  twice  that  at  100°  Cent.  In  the 
case  of  hydrogen,  the  reverse  phenomenon  of  a  rise  of  tempera- 
ture on  passing  through  the  plug  was  observed,  the  rise  being 
doubled  in  quantity  when  the  temperature  of  the  gas  was 
raised  to  100°.  This  result  is  conformable  with  the  experi- 
ments of  Regnault,  who  found  that  hydrogen,  unlike  other 
gases,  has  its  elasticity  increased  more  rapidly  than  in  the  in- 
verse ratio  of  the  volume.  The  authors  have  also  made  nu- 
merous experiments  with  mixtures  of  gases,  the  remarkable  re- 
sult being  that  the  thermal  effect  (cooling)  of  the  compound 
gas  is  less  than  it  would  be  if  the  gases  after  mixture  retained 
in  integrity  the  physical  characters  they  possessed  while  in  a 
pure  state. 

102 


BOOKS  OF  REFERENCE 

Bertrand,  Thermodynamique,  p.  66. 

Maxwell,  Theory  of  Heat,  7th  Edition,  p.  209. 

Tait,  Heat,  p.  334. 

Winkelmann,  Handbuch  der  Phytsik,  pp.  466^*69,  Vol.  II.,  2. 

Thomson's  Mathematical  and  Physical  Papers,  Vol.  I. ,  p.  333. 

v.  der  Waals,  Continuity  oftlie  Liquid  and  Gaseous  States. 


ARTICLES 

Natanson,  Wied.  Ann.,  31,  502,  1887. 
Lemoine,  Journal  de  Physique,  (2),  9,  99,  1890. 
Schiller,  Wied.  Ann.,  4O,  149,  1890. 
Rose-Innes,  Proc.  Phys.  Soc.  London,  December,  1897. 
Bouty,  Journal  de  Physique,  (2),  8,  20,  1889. 
Regnault,  Mem.  de  Paris,  37 9  579-959,  1868. 
Clausius,   Wied.  Ami.,  9,  337-357,  1880. 

A  Numerical  Evaluation  of  the  Absolute  Scale  of  Temperature — R.  A. 
Lehfeldt,  Phil.  Mag.,  April  (No.  275),  1898. 


INDEX 


Air,  Physical  Properties  of,  81. 

Air-Thermometer,  Comparison  with 
Absolute  Scale,  76  ;  Constant- 
Pressure  and  Constant-Volume,  76. 

Atmospheric  Air,  Free  Expansion  of, 
5,  26  ;  Expansion  through  Porous 
Plug,  40,  92. 

C 

Capacity  of  Gases  for  Heal.  12. 
Carbonic- Acid   Gas,    Expansion    of, 

11  ;  through  Porous  Plug,  44,  97. 
Carnot's  Function,  64,  68,  85. 
Clausius,  68. 

Combustion,  Incomplete,  3. 
Comparison    of    Air  -  Thermometer 

with  Absolute  Scale,  76. 
Compression  of  Air,  20. 
Cooling    Effect,  35,  88  ;    Effect    of 

Temperature  on,  52,  102  ;  Effect 

of  Pressure  on,  44,  50. 


D 

Density  of  Gases,  Measurement  of,  8. 

E 

Efflux  of  Gases,  Law  of,  8. 

Elasticity  of  a  Gas,  79. 

Expansion  of  a  Gas  :  by  Heat,  Con- 
stant Pressure,  77  ;  by  Heat,  Con- 
stant Volume,  77  ;  with  Exter- 
nal Work,  27  ;  without  External 
Work,  26,  29  ;  through  Single 
Aperture,  33  ;  through  Porous 
Plug,  35. 

F 

Friction,  Correction  for,  22. 


G 

Gay-Lussac,  Life  of,  13. 


H 


Heat,  Dynamical  Theory  of,  77. 
Hydrogen,  Free  Expansion   of,  10; 

Expansion     of,    through     Porous 

Plug,  52,  97. 


Joule,  Life  of,  30. 


Leslie,    Ideas    on     Heat,    11  ;    Gas- 
Thermometer,  4. 


M 

Mayer,  Criticism  of.  55. 
Mechanical  Equivalent  of  Heat,  23, 

27,  81. 
Mixture  of  Gases,  Law  of,  54,  99. 


N 
Nitrogen,  Expansion  of,  92. 


O 


Oxygen,  Expansion  of,  11,  92. 


Porous  Plug,  35,  88. 

Pressure,    Effect   of    Difference   of, 

44.50. 
Pressure,   Effect  of  Oscillations  of, 


105 


INDEX 


Rankine,  Empirical  Formula  of,  54, 
71. 

Regnault,  Formula  of,  58  ;  Experi- 
ments of,  58,  64. 

Rtimford,  Gas-Thermometer  of,  4. 

S 

Sound,  Effect  of,  11 ,  Velocity  of,  81. 
Specific  Heat  of  Gases,  77. 


Specific  Heats,  Ratio  of,  80. 
Steam,  Density  of  Saturated,  64,  84. 


Temperature,       Air  -  Thermometer. 

76. 

Temperature,  Effect  of,  52,  102. 
Thermometer,  Joule's,  20. 
Thermometer    Scale,    Absolute,    73, 

76,  85. 


106 


THE    END 


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